The psychopath's defiance, contumatiousness, impulsivity and recklessness can be easily described as forms of dysregulation. Yes, you heard me well, dysregulation exactly like in borderline personality disorder. This is one of the reasons we are considering the possibility that borderline personality disorder or emotional dysregulation disorder is actually a form of secondary psychopathy. Within the psychopath there are dynamics of dysregulation which are very reminiscent to the dynamics of dysregulation in the borderline. But while in the borderline the dysregulation usually has to do with emotions, emotional dysregulation, moods, moodlability. In the psychopath the dysregulation is externalised, in the borderline it's internalised, in the psychopath it's externalised. In other words, the psychopath projects his dysregulation via his behaviours and his behaviours impact others and himself adversely. That's why psychopaths have very bad reputation, poor guys. Good After Morning. My name is Sam Vaknin and I'm the author of Malignan Self-Love, Narcissism Revisited and I'm also a professor of psychology and today I'm going to discuss for a change. My favourite topics, psychopaths. What would we have done without psychopaths? We would have had to invent them. We need psychopaths according to many academics. They are good in a variety of professions. Military, military commanders, political leaders, surgeons and other medical professions, etc. So there's a whole branch in academia which is glorifying now and elevating psychopaths to a position of leadership. Yes, it's part of the gradual increase of narcissism and psychopathy in culture, in contemporary culture and society. But do we really understand psychopaths? Are we getting them? Do we realise what makes them tick? Many of the things we think we know about psychopaths are wrong and some of them are dead wrong. And they are wrong because the scholars and the self-imputed scholars and the self-styled and self-proclaimed experts on psychopathy had studied, usually, populations of psychopaths in prisons. And psychopaths in prison are not a representative sample of psychopaths at large. Psychopaths at large fulfil many niches. Some of them are pillars of the community. Some of them are productive members of society. They are all over the psychopath next door. And so owing to these generations of scholars starting with Cleckley in the 1940s and before him and his kind of disciple in a way, Robert Hare and so on and so forth, we had created a caricature of the psychopath, a stereotype, an animated cartoon figure which has nothing or very little to do with a garden variety psychopath. And one of the main issues where we are getting it seriously wrong is the psychopath's alleged fearlessness. We think of the psychopath as a fearless being, someone who does not experience the emotions of fear, terror, etc. The psychopath's defiance, the psychopath's contumatiousness. Contumatiousness means defiance of authority, hatred of authority, flouting the rules, breaking rules. So, contumatiousness. It's a word that makes me sound very learned and erudite and that's why I'm using it. So, the psychopath's defiance and contumatiousness are often misperceived. I repeat, misperceived as fearlessness or nonchalance. The psychopath appears to be sang-fois, imperturbable. Someone who doesn't let events, other people and the environment get to him. He is impervious. He has this imaginary membrane around him which is impermeable to the stresses and anxieties of daily life. The psychopath's main hallmark is indifference and apathy in the face of adversity. But this is not fearlessness. This is defiance. This is contumatiousness. In reality, there's a lot of trepidation, a lot of anxiety attached to fearlessness and nonchalance and defiance and contumatiousness in the psychopath's behavior. I have a video on this channel about the anxious psychopath, new discoveries, new studies in the past few years that actually undermine completely the image of the psychopath as someone who never experiences anxiety, is never phobic, is never afraid, that is absolutely untrue.  This stereotype of the psychopath is fearless. And we are talking, in this presentation at least, we are talking about what Robert Hare calls Factor 1 psychopath, F1 psychopath. Factor 1 is a derivative of the test, PCLR, I'm not going into it. It's a kind of psychopath that we are used to think of as a psychopath, without emotions, without empathy, tramples on people on the way to obtaining his goals. The primary psychopath, the truth is, and by now it had been established in quite a few studies, the truth is the psychopaths do experience anxiety and fear. One might even say that they experience their brand of anxiety and fear even more than the rest of us do. So, how come? How could generations of scholars get it so wrong? There are several important differences between the psychopath and a neurotypical, normal person.  First of all, the brain and the physiology of psychopaths are different to normal people. Skin conductance, perspiration, brain activity, heart rate, blood pressure, these are all markers of fear. When normal people are afraid, when they have a fear reaction, they sweat. Electrical conductance in the skin changes, brain activity is highly specific, heart rate increases, blood pressure in the tongue also increases, but not with the psychopath. With the psychopath, these physiological markers of fear are subdued or even absent altogether. And so we confuse the cart and the horse. We say because the psychopath's body does not react to what we consider to be fear or something frightening, it means the psychopath is not afraid. That's of course nonsense. The psychopath brain and body are different to ours, but he does experience anxiety and he does experience fear. He only experiences different to us, differently to us. He doesn't have the same equipment. He doesn't have the same machinery. Inevitably, he produces different output. Measuring the psychopath's brain activity when he is exposed to frightening stimuli, frightening photos, sudden sounds, etc. The assumption is wrong because his brain is not constructed similarly to the psychologists who are studying him. The assumption that all bodies, all human bodies are identical is counterfactual. It's absolutely not true. Massive differences between men and women and massive differences within men and within women. And psychopaths stand apart. They have a totally different brain, totally different body. In other words, to detect, to spot fear and fear reactions, fear effects related to fear, cognitions related to fear, to spot fear in a psychopath, we need to design completely different tests, tests which would be specific to the psychopath's highly idiosyncratic body and to his awry brain. The second problem is that things and behaviors that normal people find repulsive, shocking, frightening. These behaviors, these things, these circumstances, these events, other people, they elicit no emotional reaction from the psychopath. In other words, the psychopath can find himself in situations with people, in specific circumstances, undergoing a series of events that would normally traumatize, shock, frighten people, normal people, things and events that people would find highly repulsive, disgusting, horrible. But the psychopath doesn't. The psychopath's perception of risk, the psychopath's disgust response are fundamentally different to normal people. He misperceives risk where you would consider risk and be afraid. He doesn't perceive risk, so he's not afraid. But when he does perceive risk, he is afraid. That's a critical point. The psychopath disagrees with normal people as to what is frightening, as to what is repulsive, as to what is shocking, as to what is disgusting. He disagrees because he's built differently. He's a different brain. He's a different body in physiology and biochemistry and neurology. So he's a different, he's a variant, variant, variant of concern of human being. So inevitably, he doesn't react like you and others. He reacts differently. But when he does perceive threat, when he does experience something as risky, he reacts like you. He becomes afraid. He becomes anxious. Then the psychopath is impulsive. He is reckless. But when you ask the psychopath, are you impulsive and reckless? He would deny it. He would deny his recklessness. Because the psychopath perceives his behavior actually is cautious and informed and wise and measured and thoughtful. He just disagrees with you. He mis-evaluates situations and people. Or maybe you do. Most psychopaths are actually paranoid. They're hyper-vigilant and they are conspiracies prone to believe in conspiracy theories. That's one of the reasons that most psychopaths perceive themselves as victims. They live in a constant state of irrational terror, afraid of and worried about things which you consider innocuous and random. To the psychopath, nothing is random and definitely nothing is innocuous. Everything is sinister. Everything is a subtext. Everything, there are things going behind the scenes which are much more important than even the scenes. The psychopath is on the verge of paranoia all the time and very often crosses this verge. So it's not true to say that psychopaths are fearless.  These are reserved for situations and circumstances and people and events that you would consider as totally normal. And what you consider as totally normal, the psychopath would consider very, very dark and frightening. Finally, psychopaths misinterpret both internal cues and external cues, and in this sense, they're very similar to people with autism spectrum disorder. Indeed, there's a whole school which suggests that high-functioning autistic people are actually psychopaths. At any rate, psychopaths misinterpret internal cues and external cues. When they feel something, they don't know what it is. They can't give it a name. When they witness something, go interact with people or find themselves in some circumstance or environmental, within a train of events, they're not sure what's happening. Consequently, psychopaths mislabel and misattribute. This is called the error of misattribution. They mislabel and misattribute their inner dynamics. They feel something. They say, well, this must be love, or this must be fear, or this must be envy. They try desperately to slap labels on the dim stirrings within them. They're very primitive. Psychopathy is a low organization personality. It's very primitive and very chaotic. It's very kaleidoscopic. It's difficult. The psychopath is driven by urges and all kinds of impulses, and he's like a ball, a pinball, in a pinball machine. He's being pushed from the inside and from the outside, totally reactive, acting on a whim, whimsicle. So, for example, when the psychopath is actually very afraid, he's likely to say that he is very excited. He confuses fear with excitement.  Psychopaths are mirror humans. The few emotions they do possess, all of them are raw, primitive and negative. And these few emotions are inverted 180 degrees. They are mirror humans. Amazingly, psychopaths are convinced that this inversion is actually normal and common.  They believe that they're totally normal, and they think everyone is like them, and they're pretty shocked to discover that they're not. For example, most psychopaths react with indignation when the law catches up with them and places them behind bars. They don't understand what they have done wrong. They behaved as anyone else would, isn't it? Psychopaths love or they like others who are useful to them, and only for as long as they benefit from these people, one way or another. They conflate love attachment and bonding with usefulness and the receipt of services of goods. Psychopaths use the disposition and flow of material goods to gauge such sentiments. So, as long as they receive attention, in case they are narcissistic, as long as they receive sex, money, access to power, contacts, other benefits, help, advice, support. As long as they receive something, they feel that they are loved, or at the very least that they are liked, that they belong. The minute they stop receiving something from someone, they perceive it as rejection, as not being liked anymore, or not being loved anymore. And psychopaths do experience shame. It's another myth that they don't experience shame, regret, and remorse. They experience shame, regret, remorse, and even guilt. But they experience these emotions only when they are exposed as weak, as desperate, as helpless. They hate to be perceived this way. When there is incontrovertible evidence that they are less what they pretend to be, that they are not as strong, not as resilient, that they don't have any other options. Here you see a psychopath is signaling that they have no other options, that they are actually impotent, not omnipotent. When they are exposed this way, they do experience profound shame, like the narcissist. Profound shame and guilt and remorse and regret. They get angry when they cannot secure a goal. Even if the goal is self-destructive and humiliating, it's still a goal and they want to accomplish it. They lash out at people who would not or who cannot collaborate in whatever it is they set their minds to do or to be done to them. So they set a goal, the goal could be totally self-destructive, totally degrading to themselves. But they expect people to collaborate and if these people fail to collaborate, fail to perform, they get very angry. And they do regret and they do feel guilt for having failed or for having been caught red-handed. They hate to be caught. But they never feel guilty or ashamed for having hurt and having harmed other people. They rationalize, they justify their misdeeds by contorting language to its breaking point. By creating a form, instant ersatz morality, their own law. It's my way or the highway and I abide only by my own rules. Psychopaths fearlessly risk their lives, limbs and fortune, habitually and with total strangers, but are paranoid, anxious and hyper-vigilant with their nearest and dearest. It's a very shocking feature of psychopaths. They would do the most crazy things with people they had just met. They would go with these people to very dangerous and risky environments and there do very dangerous and risky things.   Intimacy and commitment are perceived as threats. A total stranger is not a threat because he or she can always be discarded. But the psychopath places herself or himself recklessly in situations which can very often do end very badly. A psychopath never says no. The psychopath only shrugs and says, why not? Before he or she engages in the most unspeakable or degrading acts. Never know. Always, why not? Why not? Do you want to do this? Yeah, why not? Even if it's self-dispoiling, self-destructive, utterly humiliating, the psychopath is very likely to say, why not? Let's do it. Without shame, without guilt and without remorse of the class, of the typical variety, there's nothing to rein the psychopath in. Nothing to control his impulses. Nothing to make him stop and think what it is that I'm doing, nothing to inhibit him. Psychopaths are primitive, twin-driven, stochastic, bug-ridden, often intoxicated machines. Psychopaths are even worse.  Psychopaths look still alive. Many of them are charming and witty and erudite and professors of psychology. And some of them, a tiny minority, are charming, witty and erudite and handsome professors of psychology. There are two of these, I think. But psychopaths had actually died in their teenage years. They had died. They're dead inside and out. They're zombies. They are the undead. They age fast. They're progeria, terrifying to behold. The psychopath inhabits an eternal present. Theirs is an eternal present. A dawnless night of the soulless.  Psychopaths are black holes. Nothing escapes, not even the psychopath. He implodes upon himself, the psychopath, and then consumes himself in an ordinary orgy of self-destruction. It is nothing short of horrifying to hear the winds of the psychopath's insanity howling in the deserted hallways of his or her vacated mind. Clearly, wrote a whole book, and it's clear that he had been traumatized by his encounters with psychopaths. The book is called The Mask of Sanity. Behind the mask, behind the bandages, the mummies, the Egyptian mummies of the psychopaths, they wrought. The psychopath wroughts and disintegrates in slow motion, unglued by a lack of scruples and morality, a void of empathy and emotions howling abyss where a human being should have been and is no longer.


Opening the windows in the morning is my favorite part of the day No One of my favorite parts my favorite part of the morning right after coffee and You guys stay here. I am once again today The milkman can't have cereal can't have our coffee Actually, we could have our coffee because we drink our coffee almost black as it is But we need just a little bit of milk just a splash of milk or it's not right We can't be in a household with no milk Therefore I have been nominated As tribute I have to go get the milk. All right, 7-eleven You were good to me last time Be good to me again you better got milk better have milk Proper English is very important. You better have milk. I hope you got milk nothing bothers me more than bad grammar I'm one of those people Milk and not candy bars milk and not candy bars Victory because we're winners all of us Together nothing can stop us and I got a Reese's Timmies, are you open today? This one keeps shutting down like sporadically sometimes it's open sometimes it's closed Stop playing with my emotions Looks like they're open today. We left the house. So mandatory Could I get a extra large steep tea with one milk and half a sugar? and could I get An extra large coffee with two cream and a shot of espresso place. Can I get it to go? That's it Super duper Ha she giggled she giggled. I got a little laugh out of her at least When you go through the drive-thru ask for it to go Someone commented that on one of my videos. They're like whenever they go through the drive-thru they always ask for their order to go Man, I got the dad jokes down Pat now. I just need to be a dad I've been practicing. This is a delicate process Usually you want to help me out? It's been a little while. I Haven't had my shaver in a while. It was in the truck there. I Actually have two shavers. I use this Remington for the long stuff and I use This other one here. What is this? I think it's also a Remington. I Don't know. It's an older one names already worn off of there This one I use for the close along the skin for the trimming because this one always grabs the hairs and pulls it This one cuts nicer on the skin, but it doesn't do as well with long hair like I said It's a delicate process Go a bit too bright I'm only the best for this face This beard Right, I don't know. What's your process or are you just not shaved? You just have you just given up? Y'all know those big Santa Beards ZZ tops Respect Takes a lot of maintenance to keep up with those things Gonna have that nice line I Think of the mustache my mustache grows really weird. It's hard to Manage it gotta put your muzzle on so you don't bite anybody. Am I right? So I've come here to refill our water jugs so that we can drink good refreshing water And not that other tap water There is a difference we prefer the bottled water to drink or so. I don't know. I don't know. I was sent here I don't know what I'm doing doing what I'm told I Guess I should have emptied my back seat first. I have a throat all in there. I don't know what's going on That's my new slogan. I like I don't know what's going on Like I was saying before the main task for today is to get all of the stuff that was in my big truck Inside our house and go through it. I think a lot of it. I'm gonna have to throw out and a lot of it I don't know where we're gonna put it. We don't have much storage space So that should be interesting. I'm definitely not gonna need all of that stuff with me Everywhere I go anymore. It's like I never threw anything out. I just Held on to it. Maybe I'll need it one day. I don't know Today is the day we go through it and I want to know how much of that same stuff You got in your truck. Maybe it's time for you to clean out your truck if you're out there on the road This is our a wonderful city hall Off on the left here Got this nice big Canada flag on it, but I got a little bit of a beef with them They don't light it up at night.  If you're not gonna light it up at night this water softener makes some funny noises Just don't mind that over there So I got to get all my stuff out of the truck I just left it in there all night because I figured it would be a nice project for today All of the stuff I had in the big truck. I'm gonna pile it all up right here Okay, and then we're gonna braid into the house. We're gonna go through it one bag at a time Sorting out what we need what we need to throw out what I need to put away and what I can still use and then finding Places for everything. This should be fun Stuck up my loves card and a pilot flying j-card here. I have two loves cards Ha twice as good Cool, so we're gonna put that there Get the wipes purse out of the way because you don't want that to get mixed up with all my junk because That is definitely not drunk. I Don't know what's all in there Does anybody know what's in their purr? I don't know. I don't think she knows what's all in there Hey, let's do this Shoe horn activated. I wanted to go live tonight, too, but maybe we'll just go live Tomorrow, which will be Thursday. So when you're watching this, I need to set it all up And it's been busy the last couple of days getting everything moved over I think I'm gonna want a warmer hat than this though This up here above you guys Put on my cousin Ed hat. Here we go And that I didn't fit up there three of those pillows were diesel's pillows Rest of that we got to find spots for all of that and attracting a whole bunch of snow All right, hope You're waiting for me Sergeant Frank on duty Keep an eye out man. Watch your six Never know what could Sneak up behind you Brits watching the classics By 1930s Christmas Alright, no procrastinating. I'm just gonna put this all onto the spare bed and we'll go through it there Glad we got such a small house. I don't carry it very far Okay, so pillows that's pretty simple. I'm gonna want to keep this one. That's mine Those are for the dogs. We'll see if we need them or not. If not What do you think diesel? We should probably keep you're saying keep them I think you can keep them main just in case Very true true That pillow is mine. Actually, you know that shouldn't go on the top of the dog But I'm gonna put it up here for now deal with that later We put this sheet over the bed just like I did in the semi truck We do that at home as well And yes, we are going to get an actual bed frame yet our old bed frame doesn't really fit in here very well It's it's right there. It's going to the dump and it's broken at the top anyway So we're gonna get a new one without a footboard so that It's a little bit more space to walk around here. It's easier to get on and off of But for now we're kicking it like teenagers and sleeping on the floor There are other things to spend money on right now other than a bed frame Like Christmas Oh, yeah, the good old vacuum Still coming handy. I'm probably gonna have to detail my own pickup Because uh, I don't think I'm gonna spend the money on a detail this month now once again Christmas We'll be careful with our money, especially now Make sure that we're gonna be okay All right, I'm gonna get everything else onto the bed there and we'll Take it from there Diesel, how about you sort through all this? Make yourself useful No, you don't like that idea Yeah, well here's diesel steps I'm guessing these will probably go in the shed I'm gonna put these out here for now diesel These are gonna go in the shed How much stuff do you guys have in your trucks? I saw a comment a couple of comments saying that there's a lot of guys out there who have Just about the same amount of stuff in their day cabs that I did in my whole sleeper truck All right, tie these all in knots too, of course Diesel, what do you think? Does this all smell pretty familiar to you? Okay An old Wolf of bread I was just gonna say I'm surprised it's not moldy, but it's been frozen in the truck for a few weeks Swiffer Look at these diesel up to put that off to the side that actually will be useful in the house Lots of plastic utensils Safety glasses More safety glasses Kleenex an empty garbage bag box with an old camera frame in it Interesting.  I've ever made for the truck. It's a cordless fan Super quiet And you just charge it up during the day video bombing me I don't think she realized that she was going video there Yeah, one of these these I got off amazon. What's it called? Uh Be one like the letter be and then the number one This was awesome for in the hot climates where they would uh Where it wasn't quite hot enough for my truck to stay running all night, but it was Uh, just cool enough that my truck wouldn't idle because I had that automatic idle shutdown This thing was a lifesaver. I wouldn't have been able to sleep without this I had several people messaging me making sure that I didn't forget my gps Don't worry guys. Karen is safe and sound. She's going to go into the closet now where she can't boss me around anymore Satellite radio. I'm probably going to transfer my membership from this radio to my pickup That's what I'm thinking. I'm gonna hold on to this just in case It's always handy to have an extra radio around Well, you remember our big plans to have steak tonight I forgot to check to make sure that we had propane So we don't have propane So we're having four men's steak in a pan This is how I used to always cook my steaks before I had a barbecue when I first moved out Put them in a pan It works because we both like it medium rare to rare anyways or used to like it with a little bit of mu in it So she likes it really rare. So all you gotta really do is sear both sides No, I like a medium rare more on the rare side More on the rare side No more mu you don't like the mu in there anymore. I like lots of mu but not Just searing on one side Okay, not like blue moon or whatever they call that Blue is it called blue moon blue something blue steak? What do I know? I I don't know what's going on Say we're having steak and potatoes uh Gotta mash those potatoes up yet and these should be done in a little while It works. I'm not going out to get propane now I'm I'm way too hungry for that But uh, I did get that milk this morning Just Throwing that out there That was me I'm a man of many talents I'm the milk man. I'm the potato man I also drive trucks Sometimes Look at this She just said just keep mashing I'm really looking forward to this Just gonna take a quick little gander inside here see if uh The inside is To my standards. I think I cooked it too long Oh, no, no, oh Show the camera show the camera She is perfect I think She's got some pretty good mu in the center yet. We might want to put her on a little longer. What do you think of this? Oh, yeah, maybe another minute It's hard to do it on the pan because it the outside always looks like it's cooked Uh, it's just easier all around on the uh, yeah, the outside makes it look like it's fully cooked Put it back on there just for a little bit Yeah, that was always the problem with cooking on a pan. I remember this now from The bachelor days Long time ago in a far away land When you cook it on a pan It makes it look all around like it's well done, but the inside is still not quite done It's it's much better cooking it on a barbecue much better, but this works When you really want steak and you're out of propane Yeah, josh apparently we're gonna have some garlic breath I think I overdid it guys Oh, well, I'm a quarter Polish really you can never overdo the garlic, right? More garlic the better keep the vampires away. That's right Are you wheezing? Keep the weasels away too He's sitting a little further away than usual, but Frank's still there. I lost my sense of smell in the wall Sergeant Frank So the steak's turned out all right not nearly as good as it would have been on a barbecue, but It was a steak So thanks for watching today everybody Uh, kind of bittersweet going through everything from on the road Sorting it all out. We still got to find places for quite a bit of stuff Uh, we're not quite done sorting through it all. There's a lot of stuff in there. Let me know down below Uh, if you think you got more drunk in your truck than I had in my truck I'd love to know Make me feel better I feel like I got a lot of clutter in there that I didn't need So we'll see you tomorrow for another video. Don't forget to subscribe if you haven't already We'll see you later


The scariest thing about narcissists as you may know I have dealt with many narcissists in my life some of them were overt narcissists while others were more covert but either way there was something that united them and it made them more noticeable it made them stand out there was something very striking and surprising about them and that is the way that they were all exactly the same regardless of their age gender or what part of the world they were from it was like the same person in a different body they all did exactly the same thing they all had the same personality the only difference was how they looked their physical appearance but at the core they all had the same habits they had the same settled and regular tendencies and practices they all had the same motivations the same arguments or reasons for acting and behaving in this part to get away and they all had the same differences the same disagreements differences of opinions or misunderstandings even though some of them were covert and others were grandiose they all had the same core issue which caused it to turn into an abusive relationship and yet they all made it seem like they don't have a problem they move on to the next person and they seem to be doing great they act confident and accomplished they have this arrogance and entitlement they're self-absorbed and they lack empathy and yet they think there's something desirable and attractive as though they're special and unique they're better greater or different than what is usual they're the only one of its kind so in their minds they're very valuable because in their minds there is no one else like them which is very peculiar and ironic because the reality is that they're all exactly the same there is nothing that sets them apart which explains how I managed to achieve over 40 million views on this channel because no matter what part of the world you're from and regardless of the age or gender of the narcissist that you were dealing with they all act and behave exactly the same way because they all shared the same core issue while at the same time appearing as though they don't have a problem as though they're competent organized and prepared and they can behave appropriately and effectively which naturally causes all of their victims to find each other in these communities because we may at first believe that there's something we can change to improve or because we realize that our feelings actions of behaviors do not change the outcome or result our choices and decisions do not have any influence will affect on the narcissist it's ineffective it never results in anything successful productive or constructive which may begin to affect your self-esteem especially when you see them moving on and they seem to be doing fine with someone else which is what they will use to try to prove to you that you're the one who is incompetent or ineffective it's all an illusion it is in fact they who have the problem they have no sense of self they're very insecure they lack self love and self care which they try to disguise by being egotistical by acting arrogant and entitled as though they don't care about other people and it's all about them which can be very confusing because it may seem as though they're in love with themselves when in fact they're just in love with their mask they're in love with their false image this disguise that they use to fool people because they want to appear to people in a certain way so that they can feel good about themselves but that's not who they really are they lack self love and self care because they're not willing to be honest with themselves and address their problems so that they can help other people and help themselves to heal and change because they're very insecure it's too painful for them to do that because they lack a sense of self they don't feel like they're enough which is why they can't deal with criticism they see it as an attack so now they have to go and blame you or someone else because they don't want to hear it they don't want to feel those emotions because they're insecure about the things they have done they have a void so everything they try to go towards does not make them feel better which is why everything you try to do to please them does not produce a favorable result it's ineffective because they're never satisfied they can't be satisfied and deep down yes they realize that they have a problem so they wear a mask they pretend that everything is okay they act arrogant when in fact it's the opposite they just don't want you to see it because they're very insecure they lack a sense of self which is why they will use you or someone else to prop up their false reality of them being this wonderful person so that they can feel good about themselves when it's just shared psychosis a fantasy a dream it has no basis in reality which is why they always need other people to validate it so that they can feel less insecure as though that's who they actually are they have all of this guilt and shame which they don't want to reflect on so they don't want you to acknowledge who they actually are unless they can find a way to project it outwards and use it to hurt you because otherwise that would be very painful for them because they're very insecure so when they feel guilt or shame they have to run away from it which means that they never process it they push it away so that they don't have to deal with whatever they're feeling because they don't want to accept that they did something bad or that they're a bad person and instead they wear a mask they act as though they didn't do anything wrong and by doing that it remains at their core to where they always feel like they are bad and when a person feels like they're bad they can't find satisfaction in anything in life they can't experience anything positive or good which is why a lot of times they will discard you first they will ghost you because they don't want you to invalidate or reject them they don't want you to make them feel bad and it may seem like they're running from a you but they're actually running from themselves because they don't want to be who they actually are they don't want to reflect on their feelings of guilt and shame or on their fears of rejection and abandonment they would rather just wear a mask if it means that they can avoid their insecurities which causes them to have these coping and defense mechanisms which are hurtful and destructive to other people it's why they're all the same it's why it's like we're all dealing with the same person in a different body because they can't be vulnerable they can't be themselves instead they can only wear a mask and pretend to be something they're not which is why they will often blame you and get very angry at you and they will manipulate and gas like you because they're trying to run away from who they actually are they're running from themselves which is why it seems like they all act exactly the same way regardless of what type of narcissist they are because they're all running from themselves so they're all miserable and dissatisfied because to experience genuine positive emotions you have to be connected to self while narcissists are driven by their own insecurities guilt, shame and rejection which causes them to respond in the way that they do and until they finally acknowledge their actions and they process their emotions so that they can heal, grow and develop nothing is going to change which is why in most cases they remain that way for their entire lives you will never see a more positive or productive side of them because most of them are never going to accept themselves they're never going to accept who they actually are which means that they're never going to accept you and they're never going to deal with you appropriately because they don't even love or accept themselves so how can they accept anyone else how can they experience genuine fulfillment with anyone in their lives which is why most of them will remain the same they're always going to be miserable and dissatisfied they're always going to manipulate deceive shame guilt trucking gas like you but you shouldn't worry about it you shouldn't see it as though you've lost this wonderful person which is how they would like you to think so that they can get supply but you shouldn't see it that way because they're not even connected to themselves which you should know from you being able to relate your situation and experiences to my videos because they all act and behave in exactly the same way so they have no identity of their own they have nothing to give all they can do is project their own and process negative emotions and traumas onto you thank you for watching if you found this video helpful please give it a thumbs up share your thoughts in the comment section hit the subscribe button to receive the notifications if you would like to support the channel you can donate at paypal.me slash narksurviva you can book a one-on-one with me on my website it's narksurviva.uk thank you for watching and I'll talk to you soon


Hi there! Welcome to our online self-access materials for Comparison Contrast Essay. Let me ask you a question first. Besides comparing and contrasting, what is the purpose of this kind of essay? Have a think about it. We'll come back to the question later. Okay, so what's in this unit? Well, we look at how to plan and organize a Comparison Contrast Essay. Let's look at an example. Say you've been asked to compare and contrast cats and dogs as pets. This is fairly straightforward. As you can see, there are a number of similarities and differences between cats and dogs as pets. Okay, so this brings us back to the question I asked at the beginning. What's the purpose of a Comparison Contrast Essay? Well, you know about the similarities and differences. Now, once you have this information, you can then start to analyze it. For example, based on this evidence, which kind of household would cats be more suited for? And which households are more suited for dogs? And if you're still unsure about anything in this unit, you can always ask the staff in the independent learning center of your university. Okay, we hope you found this information useful. Good luck with your studies!


Hello, hello everyone. My name is Laura. This is my channel Laura's Little Library and welcome to today's video Which is a cum book shopping with me video So obviously I am in the car. I just finished my I just finished my work shift and I have zero patience I am Going to the bookstore Because there are a couple books that were released yesterday that I I really want to pick up and Initially, I was gonna go to the bookstore this weekend and I'm still planning on going to the bookstore this weekend But right now like I said, I have no patience no chill And so this is for my May book budget and May is also my birthday month. So It's a little different. It's a little special It's fine. Hopefully I can still keep myself control Yeah, when I get home, I'll do like a mini haul and Of what I get today and then what I got at Goodwill yesterday And then you can come along with me again this weekend for even more books. Hopefully So we are back from Barnes & Noble and I have freshened up a little bit and kind of come home and I'm going to go through all of the books that I got. I will definitely say I was unsupervised and I definitely lost Self-control very much though. However, I will say that so this is my book shopping for May And so while it may have gone over my book budget for the month It is also my birth month. May is my birth month. So Happy birthday to me. First things first. I went to Goodwill the other day with a friend of mine And she was actually looking for a childhood book of hers to Cut up and put on her graduation cap. And so I thought we're in the book section anyway You never know what you'll find at like Uthras stores Like bookshelves and I actually ended up finding Language of Thorns by Leigh Bardugo So this is kind of the collection of stories of the Saints and just kind of some Grisha verse lore and mythology a little bit So I thought this would be really fun to have and to read about and really just to kind of add to my collection Yeah, I thought I'd pick this up next up I got a book that I just finished reading and that is Nettle and Bone by T. King Fisher This is a book that I really enjoyed I think what I like most about it is the unique elements that this book did it took your typical fantasy idea, but really made it its own So I I'm very happy to finally have this on my shelf. I got one dark window by Rachel Gillig This one has just been capturing my attention everyone who's talked about it has made it sound so interesting but for different reasons, so I am going to take a risk And uh, I'm excited to read this. I kind of know what it's about. I kind of don't So Yeah, I thought this would be a really fun one to try out Maybe I might save it for spooky season. I'm not completely sure about that But I feel like it would be a good like spooky book to read. The next one is a whole trilogy I cannot believe I did this City of Brass Empire Gold and Kingdom of Copper by SA Chakraborty. So this is like one of the big Chunky trilogies that I've been wanting to read for a long time now but I I wanted to sit down and read them all at once read one two and three And so I finally just bit the bullet and was like, all right I'm gonna get the trilogy. I'm gonna read it this summer. I really I have a goal This year of catching up on some of the fantasy series and books that I've been wanting to read But haven't been reading because other books are shorter or more available or Whatever, so I'm getting started I'm I'm gonna read these hopefully this summer and it's a pretty cool Like I think it's like a desert fantasy and the desertathon is in May. So perfect I don't know how fast I'll be able to finish these but I will do my darndest. That's for sure Moving on to romance of the Backlog of books that I've wanted to buy. Well, this one is a new book on my list of books I wanted to buy but it's not like a new book That is Terms and Conditions by Lauren Asher. I got the fine print. I read it and I absolutely Loved it. I devoured it in like a day. Maybe two days Um, so I really wanted to get the rest of the billionaire Or the dreamland billionaire trilogy the romance kind of companions and they each I think feature a different trope so Yeah, I'm excited to read this one and see what comes next for the next brother Now speaking of romance, we are also going to get into some of the New release books books that just came out that I could not help myself and I had to get Right now. I already showed you this Uh, Emily Henry's the happy place This came out as a filming yesterday So, yeah, this is technically late April but not the point. Um, I I've really enjoyed a lot of Emily Henry's other books I have her other contemporary romance books and I like them I'm a little annoyed that this one is hardcover. I understand that she's going through a different publisher and they do things differently but like I have all of her other books in paperback and I'm not waiting a year to get this on softcover Especially since the hold for the audiobook on the library is probably also going to be a year So I bet the I I just did it. I just I got the hardcover for the happy place by Emily Henry It'll be a great summer read Another great summer read but in a very different way that was just released either today or also yesterday Is this delicious death by Kayla Cottingham? I So I read Kayla Cottingham's other book, um, my dearest darkest and I really liked it I thought the book itself was a great debut novel and that I think this author is one that's going to grow And the books are just going to get even better And then when I heard this book was coming out, I got all excited. So I went and I read the summary and I was like, ooh cannibalism Not something I've ever wanted to read But I am taking a leap of faith because I am invested in this author with, you know their one other book that they've published And it's you know, it's why a thriller and it's queer. So I don't know. Plus it's like set to like summer kind of music festival vibe. I think like Yeah, very summary and Thriller-y and queer. So you know Who knows I don't think this book will change my opinion on reading thrillers in horror with cannibalism But I don't know if I'll actually hate this book Because of it at least because there was quite a bit of body horror in her other one And I didn't mind it. So I'm hoping that the cannibalism will just be like A thing I don't mind and I'll enjoy every other aspect of the book Oh, I just realized I haven't been checking for stickers on any of these, but I don't think I don't think a lot of these have stickers. I think it's just these new releases that I'm going through I have stickers that I'm trying to Yeah, yeah, okay Now another book by an author that I am like Kind of an autobi author even though it's still pretty early in their career The author is hannah witton and the book is the fox globe king. So hannah witton wrote One of my favorite duologies, which are also just some my favorite dark fantasy romance of all time And so I knew when the fox globe king was coming out. I knew I had to read it. I read the premise I loved it. So Yeah, I I knew that I was gonna want to get this as soon as it came out and it came out earlier I think like in march I just have so many good books that I'm gonna read this summer like I I would really love to read all of these books Through the end of summer. I think every book is summary in its own Way, so I just love this color cover like there isn't much color But I kind of love it. So Final book that I got from Barnes and Noble that is a new release Is one that I've seen other people talk about and it's like the perfect summer read and I'm really excited about that But I didn't honestly think I would actually Purchase it or at least not without reading it first And I haven't really been putting in a lot of effort to get like the audiobook or this book from the library or anything like that So I was kind of surprised that I bought this But I don't regret buying it. I just have to get the sticker off first Sometimes these stickers come off like really easy and sometimes they just don't Oh, it's an easy one Huzzah, anyway, and that is the Adventures of Amina Alasrafi and this is by Shannon Shakroborty And this is like a piratey rescue Kind of book and so, you know pirates It's a great summer read and there were a bunch of other books. I was like, oh, it's Mermaid II I want to get it and I was like, no self-control self-control Which obviously I still fail that but I I'm excited for this one. I think I'm gonna enjoy it. It's just gonna be a fun adventure with pirates this summer so So those are the 11 books that I impulsively bought Initially, I was also thinking of going to half price books this weekend because It's my last month in Minnesota and we do not have half price books in michigan So I will no longer have like a good place to get discounted books Like like half price books, but after what I pulled today I don't think I can justify that and I'm not super heartbroken about that because I've been going to half price books pretty much every month that I've been here and it's gotten to a point where I'm pretty familiar with the books that they have like obviously they're always getting in new books and you never know what you're gonna find but I don't feel like I'm missing too much by not going this final month I just hope that they can open one up in michigan preferably Close ish to where I live or where my parents live Or at least where I'm moving to Versus where my parents live. I mean that that would be nice, but Those are all the 11 books Thank you so much for watching if you like this video and give it a thumbs up comment down below Do you shop seasonally or monthly like you buy books because it'll be great for the upcoming season or Like I want to learn about your book shopping habits because I want to know if I'm the only one who loses control like this I don't think I am but it's always just nice to know that I'm not alone Also, I have bookish social media link down below that you can follow me as I am reading these books But as I am reading them, I will also continue to make videos So feel free to subscribe and definitely hit the bell to be notified when I post because I'm about to have a very busy next couple of three months Um because I will be moving to a different state and then going on vacation for two months So I'm gonna do my best to have at least one video a week go up Ideally, I would love to have two videos a week go up as I have been doing this whole year And pretty much all of last year They could be great if I can continue that but I make no promises But I will definitely try and have at least one video going up a week over these next three months So just hit the bell to be notified so that when the video does go up You know and you can watch it and maybe give that video a thumbs up. I don't know who knows But yeah, that is all that I have to say. I'm gonna go lovingly put these books Where they belong because I don't think I've read Any of these I have not which has been a goal of mine is to catch up on books that I have already read and want to own There is one book here that I've read so I can put that one on my shelf at least Which is probably good because these shelves are starting to get a little full Uh, but that's what new bookshelves are gonna be for, right? So if you're interested in new bookshelves Subscribe. Okay. I'm gonna stop blabbering on. Thank you so much for watching the video again And until I see you all in the next one. I wish you happy reading


Thank you. Thank you for the introduction and thank you very much for the invitation to speak here. It's a really great honor for me to be speaking for this conference in honor of Arthur. So one of my favorite theorems from when I was a graduate student is the theorem in chapter 8 of Berthela August. And what I want to explain today is some joint work with Matthew Morrow and Peter Schultz, which sort of really uses the construction in chapter 8 of Berthela August in a crucial way. So I'll mention what the theorem was when we get there. Okay, so I guess it's a joint with Matthew Morrow and Peter Schultz. And the setup, so I want to talk about a certain integral columnology theories and relations between them. So the setup I'll fix once and for all as the following. So C is going to be some complete an algebraic closed extension of Qp. And so for example C equals Cp. Oc is the ring of integers and little k is the residue field of Oc. So this is a valuation ring and it's a perfect field. And then you also have the ring of vectors of k. And then finally the sort of main object is going to be a proper smooth scheme over Oc. So actually everything I'm going to say already works in the context of formal schemes. So if you like you can work in that context, but it's interesting enough in the case of smooth project. Schemes over Oc, so things with good reduction. Okay, so in this setup, there are certain co-mology theories that we know about eventually. But nothing I'm going to say. I think, yeah, I want to... The paper on the archive, you assume I think projective smooth rather than proper smooth. No, no, we assume proper smooth. Right? I thought it was a proper smooth formal scheme. Okay, so since everyone already knows the paper, maybe I shouldn't talk about it. Classical piatic co-mology theories associated to this picture. So there's three of them that I want to focus on. So the first one is etalc homology. And so by this I mean the etalc homology of the generic fiber. We'll denote by X of C and the coefficients are in Zp. And so this lives in the world of finite Zp modules. And so in the algebraic case, the fact that it's finite is classical. In the formal scheme case, it's more recent. And then it does a Galois action. All the constructions are going to be Galois covariant. So if there is a Galois action, then we'll get a Galois covariant statement. So this is a theory coming from the generic fiber. There's a theory coming from the special fiber, which is crystalline co-mology, which we heard about in the previous talk. So this is the crystalline co-mology of the special fiber. Relative to W. And then the Frobenius and X on the special fiber induces an endomorphism of this. So this lives in the world of, let's say, finite P modules over W. So it's a finite module over the ring of width vectors, and it has this endomorphism given by Frobenius, which will be called P. And then the third one is sort of... So I have the generic fiber, I have the special fiber, and then I'm going to use the integral model. So here's the Dirac homology. So this is the Dirac homology of this morphism. And so this is, again, a finite dimensional... Well, it's a finite OC module, and it has a filtration coming from the Hatch filtration. So it's a finite filtered OC module. So these are the three theories I want to focus on, and then we know that there are sort of various comparison isomorphisms relating different subsets of them. And I'm not going to spell them out right now. Like, for example, Fontaine's Dirac conjecture tells you that A and C are essentially the same information after you extend scalars to B Dirac. And A and B is the crystalline conjecture, and then B and C is the birth of August theorem relating crystalline with Dirac. Okay, so the goal for what I want to do today is... I want to sort of try and explain a single picture, or a single homology theory of which all three of these are specializations. So realize all three are specializations of the same, of a single theory. And already it's clear if you want to do this, you need something... So in each of the previous cases, the ring that I was working over was either Zp or W or OC, so it was a dimension one ring, it was a valuation ring. And if you want something that's going to specialize over two different valuation rings, it needs to be at least two-dimensional. And this ring is sort of the main sort of playground in this talk. So it's Fontaine's ring A and... And sort of going to be the object over which everything lives. And let me sort of... Let me tell you what it is. So the definition, it proceeds in two steps. So first we define what I guess nowadays we call OC flat. It's by definition, you take the ring of integers of C, reduce it mod P, and since now you have a ring of characteristic P, it makes sense to talk about its perfection in the sense of inverse limits. So this is the inverse limit over Frobenius of OC mod P. So it turns out, by non-trivial theorem, that this is actually itself a really nice object, so it's a valuation ring now in characteristic P with an algebraic equals fraction field. So C flat is going to be its fraction field. And so roughly what's happening is that when you take your valuation ring and reduce mod P, you sort of lose the dimension, so this is a zero-dimensional ring, but it has tons and tons of nil-potens. So when you pass through the inverse limit along Frobenius, those nil-potens sort of build up to give you an extra dimension. And that's what OC flat is. And then the ring A-inth is the deformation of this to characteristic zero. So the ring of it after is OC flat. And this is a perfect ring of characteristic P. So taking the width vectors is a really nice thing to do. And I'll call phi the Frobenius you get by thinking of it as the width vectors of a perfect ring. And so this is going to be the basic object we're going to be working with. And I want to explain how it's related to the three rings appearing on the first board up there. So in order to do that, I'm going to choose coordinates. And this is not strictly necessary, but it just makes certain constructions easier. So I'm going to choose P underline in OC flat, which is a compatible sequence of P power roots of P. So you just choose a compatible sequence of P power roots of P in OC. And this gives you an element of this inverse limit, which I'll call P flat. And then by taking Teichmuller lifts, you also get the element, bracket P flat, living in A nth. And then the basic slogan, which I'll try to make precise, is that A nth is sort of, it's kind of like a two dimensional regular local ring and the two coordinates are P and P underline. And I warn you right now that what I'm about to write is completely nonsense, but that's why it's a slogan. So it's a two dimensional regular local ring. And the parameters are P and P flat, sorry, P, bracket P. And there are theorems that say that it behaves like such a ring, but for example, it's not two dimensional. It's not regular because it's not an aetherian. And those two are certainly not parameters in any reasonable sense. But anyways, that's the philosophy. And the reason this is related to the previous slide is that because of the choice of coordinates, you can define these three explicit sort of rank one quotients. So you get three divisors. So the first one is where you kill P. So if I take with vectors of a perfect ring and then I kill P, I just go back to the ring I had earlier. So I have OC flat. The second one is where you kill P flat, so the other parameter. Sorry, I keep saying keep P flat, but I mean bracket P, bracket P underline. So this is not literally where you kill to get here. Here you use the fact that the width vector construction is factorial. And there's a map from OC flat to its residue field, which is k. And so passing to the width vector is you get such a quotient. It is the case that this element is in the kernel, but for example, so are all of its P power roots. So this element does not generate the kernel. So this is even worse things in there. And this is independent of any choices this one. Yeah, so the map is completely independent of the choice. I'm just to write it down. Yeah, the map is what I said. It's the functoriality of the width vectors. And then there's a third map, which is Fontaine's map theta, which goes to OC. And here you kill the difference of the two coordinates. So I'm killing the horizontal direction, the vertical direction, and then the diagonal direction.  And this literally is true in that this generates the kernel. Again, it's independent of choices, if you were right. Yes. So the map is totally independent of choices. This is just one convenient choice of representatives for elements in the kernel. Is there a functorial definition of this map? You can define it, for example, using the cotangent complex formalism. In this formula, it was E p and mod p. There is such a map, and therefore it lifts to characteristic zero. There are more explicit definitions. OK. So I want to work with this ring. And so I want to actually draw a picture of what it looks like. And so this is a cartoon of Speck-A-Inf. And so if you've seen the cartoon Sholza has been drawing at Berkeley a year ago, I warn you that this is different from the one he's drawing. I prefer this because it illustrates one feature that's relevant to what I want to talk about here. So this is really a picture of Speck-A-Inf. So I'm going to draw the generic point. So here's the generic point. Here's the close point. And here are these three quote unquote height one points that I'm interested in. And I will label all the points with the corresponding residue fields. So extensions of residue fields. So the residue field at the close point is K. This point corresponds to the fraction field of W. So W join one over P. This point, so it's the generic point of this quotient over here. The point in the middle is the generic point of OC. So C. And then the last one is C-Flight. And then there are specializations relating them. So I'm going to draw an arrow whenever there is a specialization. And oh, yeah, I guess I didn't label the generic point. So it turns out that the generic point sits inside a beater arm. So I'll just label it by beater arm. So that's a rough picture. I also want to go further. So I want to not only label the points, I also want to label the specializations. So for example, this specialization corresponds to the ring W. Meaning this quotient is to W of K. This specialization corresponds to the ring OC-Flight, which is the first one over here. And the other one is the other one. So this is OC. And so in terms of this picture, what's going on? So let's see. Let's write down. Maybe I want to label one more or two more. So this specialization, you can think of it as being W of C-Flight. Meaning those are functorial map from W of OC-Flight to W of C-Flight. And the quotient of the special point, the field of the special point is indeed C-Flight. So this is where W of C-Flight comes in the picture. And this specialization here, after completion, is what's called B-derarm plus. So this is a valuation ring. And its fraction field is B-derarm. And so the only thing missing is this guy. And this guy is kind of weird, so I don't want to name it. It's sort of closely related to the fact that the kernel of this map is not generated by just P-Flight. There's lots more junk in there. OK. So in terms of this picture, what is going on? So crystalline homology is living over here on W. So crystalline homology. D-derarm homology is living over OC. And a telecomology, well, it turns out that there's a pretty nice way of thinking about it is living over here, which I'll explain when I write down the theorem. And maybe, OK. So these are the existing three theories of living. And what I would like to explain is a picture of what sort of fills at this end. So we want to construct something that lives over all of A-ins. And it's going to have the correct specializations. Is there any interest in that? It just might be a theory of OC-Flight. Yes, it's very interesting. So I'll comment about that theory once I write down what the result is. That's somehow like where the new information is coming in. What about mysterious errors? So the point is if you label the specialization by the complete local ring at that point, then this guy just turns out to be W of 1 over P. Because the kernel of this map satisfies that M equals M squared. So that's why it's kind of weird. Are there any other questions about the picture? OK, so I'll have to figure out how to erase. OK, so here's the main result. I think this was section two. Well, I guess it was section three, probably. I think it should have been three. So there should be four. I'm following my notes. So results. And so the main theorem is that what I said we are going to do, we can do. But let me sort of say it in a rather precise and maybe slightly long-winded way. So again, I remind you that our setup is x over OC is proper smooth. And to this data, we can associate or can functorily attach a complex, which I'll call r gamma sub A of x. So this is a perfect complex of modules over the string A and f. And it has an extra structure coming from Frobenius. So plus a map phi sub x from the complex to itself, which is Frobenius linear, semi-linear. A is A and f. Yeah, sorry. Yeah, thanks. So it's phi semi-linear with respect to the phi on A and f. And it's an isomorphism after you invert this element that I had called psi earlier. And maybe this is not so important for now, but we'll come back later when I make a remark about this. And an isomorphism after inverting this element psi, which I remind you was a generator of the kernel of theta, with the following realizations. So satisfying. OK, so in my notes, I have the etal one first. So the etal realization is the fact that this construction recovers etalc homology. And the way it does is that you have to go to W of C flat and then extract a ZP module out of it. And here's how it works. So there's a canonical isomorphism putting this complex scalar extended to W of C flat. So restricted to that height one specialization over there. And etalc homology, ZP coefficients, also scalar extended to the same ring, which is compatible with Frobenius. So there's a Frobenius on the left-hand side coming from the fact that there's a Frobenius on each factor.  And what this means is that you can recover the etalc homology itself as the phi in marines. So this is by a theorem of cats, I guess. So if you're interested in the etalc homology, not just a scalar extension, then you can recover it by the following formula. So you take this complex over A n, you extend scalars to W of C flat, and then you sort of do phi equals 1. And if you sort of invert P, then you really do phi equals 1 on homology. Otherwise, it's the derived version of that construction. Okay. I think that phi minus 1 is a surjective on... So when you go from ZP to W of C flat, it's a flat extension and the Frobenius minus 1 is... I think... So you're saying the derived construction is not necessary? Well, for homologies, it should get this... Yeah, that's... Yes. I just wanted to be safe. Yeah. So cats' theorem is that if you have any perfect ring of kerosic P, ZP local systems on spec of that ring are the same as modules over the width vectors of the ring which are isomorphic to themselves after pullback along Frobenius. And so, I guess, yeah, that's a good point. So I want to point out that once you make the scalar extension, this element C becomes invertible. Because remember, in this picture, the zero locus of C is over here. So when you base it over here, there is no zero locus. So the Frobenius is actually an isomorphism on the nose, not just after inverting something. And so you get a unit root crystal on W of C flat and thus it corresponds to the local system. Okay. So the others are more direct. So the crystalline realization is exactly what you might expect. So you take our gamma A of X and you scalar extend to W of K and you get the crystalline complex. Again, as females. And so, for example, what does this tell you? So if you know that on the left-hand side, Frobenius is an isomorphism after inverting C. Now if you stare at the picture, the zero locus of C is over here. So when I restrict over here, that just means it's an isomorphism after inverting away from the close point, which is the statement that Frobenius is an isogeny on crystalline comology. And then the drom one. So again, our gamma A of X answered over A of N. And now there's a choice. So I think the way we wrote the announcement, there's no Frobenius twist, but I'm going to twist it. So I base the angel on phi first and then specialize to O of C and then I get our gamma drom of X over O of C as filtered modules. And I will explain or maybe not how the filtration comes about later. And I guess I want to emphasize, maybe this is clear from the title, but that everything is integral and on the nose. So you get some statements about torsion from this. Okay, so corollary. So we got to write two of them. So the first one is if you can ask what the relation is between the dimension of etalcomology with Mach-P coefficients and the dimension of crystalline comology with Mach-P coefficients. So the crystalline comology of the special fiber relative to K, which is also just the dimension of the dromcomology because drom is crystalline. And then what you get out of this is that there's an inequality this way without any assumptions on ramification. Sorry, my shoe laces are coming and done. And then there's an integral lift of the statement. So this is a Mach-P statement and you can ask what happens integrally. And integrally, what you can say is the following. So if the crystalline comology is torsion free in degree I, so is etalcomology in the same degree. And x is x. Ah, yeah, sorry, thanks. Otherwise it would not be so interesting. Okay, so maybe I want to make one comment. So first of all, the inequality in one is strict. So there are examples where there's genuinely more crystalline comology than there is etalcomology. So you can't expect to do better. And this is more or less the only direction that is reasonable if you sort of have some defamation theoretic picture in mind. And indeed that is the case. And likewise, there are examples where the crystalline comology has torsion, but the etalcomology does not. In fact, we wrote one down in our paper. It's a three-fold incursive two. And so this is the only thing that could be reasonable. And maybe I'll sort of just explain the proof of one. Before that, can I ask you a question? Yes. The difference in torsion and crystalline comology and in the Dirom-Cohomology, there are Ecke-Dahl's example, which shows that the ramification is bigger than p minus 1. They need not be the same. Do you have any way of incorporating that? I guess the short answer is no. I don't know what the relation, like a precise bound for the discrepancy between the two. I've been asking people if it's reasonable to expect that the Dirom-Cohomology always has less than or equal to torsion than crystalline comology. But I don't know the answer to any of those questions. But if the Dirom-Cohomology is torsion free, it's not enough to know there is no implication, other implication. So all the implication between such and such in torsion free or something else is torsion free is in what you wrote that you have examples showing that other implication of torsion free is a lot more. The only implication I have a counter-example to is the other one, the converse to this statement. So the implication that if Dirom is torsion free then... I don't say anything about Dirom. Sorry, I mean I guess I don't say anything about Dirom. Because all of them are torsion free, it's just an American thing, which is the same. It is true, I can't think on the fly, I think it is true that if all the Dirom-Cohomology groups are torsion free, then in fact, so are all the HL-Cohomology groups. That follows from the proof. I don't know about a single degree how that argument would work. And the reason I want to mention the proof of one is exactly this point that Arthur raised. So you consider what happens over the new specialization that you gain, namely the one over OC-flat and use semi-continuity. So semi-continuity for this base change. So the point is this is a perfect complex over OC-flat and whenever you have a perfect complex over some ring, the dimension of the special fiber, the dimension of HI of the special fiber is always an upper bound for the dimension of HI of the generic fiber. And that's exactly what one is saying. But this ring is a notherian, right? OC-flat is not a notherian, but it's not so bad. It's a valuation ring of rank one valuation. It's still okay to use this notion. Yeah. I mean, for example, you can do some approximation argument to reduce to the notherian case. Okay. Yeah, she used these words. I'm going to make some remarks about the theorem. So maybe the first remark I want to make is that in fact, when the crystalline chromology is torsion-free in the setting of two, you can actually say something finer. So if HI-chris is torsion-free, then this HI of this complex over AN is itself a finite free module. So what you have is a finite free module over AN together with the self-map fee, which is an isomorphism after inverting C. And these gadgets have a name. We call them Broi-Kissen modules. And he proved a very interesting theorem about them. So the theorem far proved is that if you have a Broi-Kissen module, then the crystalline specialization is determined by the other information. So in particular, what that implies in our setup is that if you're in the torsion-free case, then the crystalline chromology of the special fiber is a functor of the generic fiber, which is not easy to see from the definition. Okay. And maybe for the second remark, I need the most space. So the second remark is about how the proof goes and the way the proof goes is that you construct the homology theory by first constructing an appropriate sheaf and taking its homology. So more precisely, we construct a complex which we're calling A omega x, which is a complex of sheaves on x of AN modules together with the Frobenius such that this homology, our gamma sub A of x, is just hyper-chromology of this complex.  A tall or pro-atall, I guess, since it's some limit thing. Yeah. So a constant sheaves with coefficients in A and f. And this complex of sheaves actually has very interesting properties. So there are two specializations that are, at least I find interesting. So the first specialization is related to what happens in the Diron specialization in the theorem. So if your base change along the map from A and f to Oc, which is Frobenius twist of theta, so the same one that showed up in the theorem, then the complex you get is really the Diron complex. So this is the Diron complex of x over Oc. In particular, it's a complex whose terms are given by differential forms and the differential is not Ox linear. It's just linear over the constants, which is Oc. But you can do something else, which is you can specialize when you don't twist by phi. So if you do that, at least if I got my twist right, then you actually get a complex of quasi-coherent sheaves. So in fact, you get a perfect complex. So it's a quasi-coherent complex on x, whose ith-comology group, or sheaf, is given by omega i.  Formal scheme. Formal scheme. Yes. So the x is a special phi? Yes. Yes. So this is the Diron complex of the formal scheme over Oc and differential forms for the formal scheme over Oc. And so this is a quasi-coherent complex. The differentials are all linear. And so this is kind of this mixed characteristic version of the Cartier isomorphism. So in particular, if you specialize both to the residue field, then you get the Cartier isomorphism. So you don't. It's not the wrong. It's not the wrong dip. OK. So I want to point out that this is the complex that somehow is responsible for the hot state filtration, menu invert p. So there's a somehow close connection between the two, which goes through this gadget over here. Again, then finally, the third remark I want to make about this is that there's a specialization in court. The complex totally decomposed in the sense of? So I don't know if there's an analog of the DeLine or Luzi theorem in general, but what is true is that if you just look at the obstruction to splitting off h0 from h1 in the one truncation of the complex, that measures the obstruction to lifting the formal scheme to a2, a-inf mark c squared. So the square zero extension of Oc relative to Zp given by this length two quotient of a-inf. And the obstruction to lifting across that extension is the extension class that's showing up here. So how can you be, you can have, when you tend to be small k, then the first line is there is an extra four venues, but how can you then have a quasi-current complex and when you tend to follow by some four venues, you get a drum complex which is not all linear, so I don't know, there seem to be something strange here. Well, it should realize the statement that the Frobenius push forward at the drum complex is that the total fiber has homology groups given by omega i of x over... And this is a generic fiber, so you did not... Well, this is integrally. Maybe we can discuss this after the talk. I get confused about Frobenius with, like, all the time when I think about this, so it's quite possible I have something off by a sign. Right, and then the third specialization which I wanted to mention is the a-chris specialization. So in this picture, there is yet another period ring that's floating around which is sort of the dotted arrow which maybe is not so visible, which is sort of a speck of a-chris, which is where you get when you join divided powers with the kernel of c to a infinitiatically complete. And there is an analogous statement over there. So r gamma a of x tends to over a... So again, there's a Frobenius twist, I believe, with a-chris is the crystalline homology of x relative to a-chris. So this is the homology theory that we already knew interpolated between the crystalline homology, the special fiber, and the Dirac homology, the generic type of the integral model. And the theorem is saying that there's somebody to extend it across all the things. So all these are isomorphisms or almost isomorphisms? Quasi-isomorphisms? No, almost. Okay, so those are the results, and now I'd like to explain what goes into constructing this object. So this is an algebra object? Which one? A omega x? It's an e-infinity algebra. Yeah, it's not a dg-algebra. So one of the main tools going into the construction is this gauge transformation business from Bertha-Logos chapter 8, so L-Ada. That's what it's called. It's a killing torsion in the Dirac category. And so the basic goal is the following. So this section is going to be kind of abstract, unrelated to the attic things. So let's say A is a commutative ring, and F is an element of A, which is a non-zero divisor. A question you could ask, sort of a naive question, you could ask is if there is a way to take a complex of A modules and systematically kill all the f-torsion in its homology. And this recipe should be somehow independent of the quasi-isomorphism class. So it should work at the derived level. So the goal is to kill f-torsion in some complex hi of k, in hi of some complex k, functorially in k. And this is not really possible if you try to do it using just nice exact functors, but I will nevertheless explain why it is possible. So the key definition is the following. So I'm going to define a functor which does this job, and to define the functor, I'll first specify what it does to nice objects, and then you resolve everything by a nice thing. So the nice objects, in this case, are complexes of flat modules, or really you just need f-torsion free. And then you do the following construction, which is denoted a to sub f. So this is an example of the filtration of the Kale for the f-addict filtration. And so you construct a new complex whose term and degree i is the set of all elements, alpha in the original complex and degree i that are divisible by f to the i, such that the differential is divisible by f to the i plus 1. You need the second condition in order to get a complex. And so this defines for your new complex, a to sub f. And then the theorem is that this recipe passes through the right category. So theorem, applying it to flat replacements, say, gives a functor from d of a to d of a, which I'll call l-ada with respect to f. It's not a phi with ki, it's a p and plus i or something like that. Well, you can define and you can think of the input as a filtered complex given by the f-addict filtration, and the output is a new filtered complex. And what I've written down is a 0th step of the new filtered complex. Do you need some boundedness in the direct category for the value of i? Not for this construction, no. But I mean, for all what you're going to do, it's going to be bounded below. It's going to be bounded. And it's going to be really nice, but... If I can do, like, f to the i, k, i. Of course, i is... you can allow formally i to be... You can allow it to be negative, which is why you need at least f torsion free. Yeah. Yes, actually, let me do an example where i is negative. And so the remark I would like to make is that this function is not exact. So it's a function between triangulated categories, but it doesn't take short exact triangles to exact triangles. And here's sort of y. So let's do an easy example. Let's take a equals zp and the element f to be p. And consider the complex k, which is just z mod p, placed in degrees zero. So this is... We have to choose a flat replacement, so this is quasi-isomorphic to this two-term complex. It's a multiplication by p on zp, where the right-hand side is in degrees zero. And so when you apply L8a to it, L8s of p of k, you're supposed to apply 8s of p to this replacement. But if you apply 8s of p to the replacement and you think about what the indices mean, it means that in the first court, in the first entry, you're allowing denominators of p. And in the second entry, you're not. So this looks like the complex, which is one over p, zp, mapping by the same differential to zp. And this is zero, quasi-isomorphic to zero, because it's an isomorphism. But if you do the exact same combination for z mod p squared, it's not zero. So you end up getting z mod p, just because everything looks the same except this differential is a p squared. And so there's a z mod p in degrees zero and so this is why it's not exact. If it was an exact function and it killed z mod p, it would have to kill z mod p squared, but it doesn't. And this is really crucial for what we are doing. I guess to go back to an earlier question. So you can prove that L8a is lax monoidal. And so in particular, it takes algebras to algebras. And that's why the answer to Martin's question from earlier is yes. Okay. So how do we use this? Lax monoidal. So a function is lax monoidal with a tensor f of b as a canonical map to f of a tensor b. It's enough to make algebras go to algebras. So the construction is going to depend on a choice. But I mean, the actual construction does, but the output doesn't. So I'm going to choose, sorry, I remind you again that x over oc is this proper smooth formal scheme and the construction is local. So let me just say it's smooth. Formal scheme. In order to do the construction, we are going to take a nearby cycle and a function applied to a certain sheaf and then modify it using this L8a construction. So I need to choose an element f to do the L8a and for that I choose the following. So epsilon underline is a compatible sequence of p power roots of one. So trivialization of zp of one, if you like. And like before, we can think of it as an element in oc flat. So earlier I had p underline and now I have epsilon underline. And the key element here we're going to use is epsilon minus one, which is an element of a. And so maybe I just make one remark about this. So one thing you could do, so I guess I should pick my normalization so I think the way I'm doing it, I want epsilon to start at a primitive p through to one rather than starting at one. So what this means, I think, is that if you do phi of mu, well, it's a compatible sequence of elements here. Yeah, but you just have to be sure where you're starting. Okay, so what I want is that when you apply this map theta to it, you get one minus a primitive p through to one minus one for mu. So it's not in the kernel of theta. And it's the closest thing that can be there, but it's not. So if you do phi of mu divided by mu, this makes sense, and this is actually a generator of the kernel of theta. And this is the relation to the previous, to that picture. So this could play, this is equally good as the element c I had earlier, which is p minus p under a line. Okay, so, I mean, if you're familiar with computations of nearby vanishing cycles in the Piatic-Hoch theory approach sort of due to faultings and then Peter, this element shows up quite prominently because you're essentially trying to do group invariance under some actions and the way you can do group homology is by gamma minus one or gamma as a generator. So that's roughly where this object is coming from and what we're going to do with it is the following. So step one. And the construction is in two steps and the first step is you get an almost correct thing and then I'll correct it in the second step. So this is almost correct version. Yes, of A and oh, A omega, X. Okay, so we're going to use the nearby cycles map, so let me give it a name. So nu is the map that goes from, or either the per-atial side of the generic fiber to the etal side of the formal scheme just given by the fact that you can pull back an etal sorry, this is a map of the corresponding tau-point. The pullback function just says that an etal cover of a formal scheme gives you an etal cover of the generic fiber. And what we're going to do is we're going to set A omega X to be the following. So this is A omega X prime because it's almost correct. So one thing you can do is you can do our new lower star. So you can push forward along this A nth, but really the sheaf-ified version of A nth on the site. So the construction of A nth makes sense for any ring. It doesn't have to POC. You can always reduce any ring mod P. You can pass through the inverse limit perfection along for bannies and then you can do the width vectors. So you can perform that construction as a sheaf on the per-atial side and I'll call that sheaf A nth comma X and then you push forward. And okay, so that's complete nonsense if this is the first time you're seeing it. I'm sorry, but I wanted to give an actual definition. And then this guy is sort of not good because for example, for bannies is an isomorphism on nth. So for bannies is an isomorphism on this complex and it certainly is not going to be an isomorphism on our A omega. So you're going to modify using L eta. So do L eta sub mu off this. And the for bannies on this guy which was an isomorphism now induces a map which is not an isomorphism. It just induces an endomorphism. So this is an object of the dry category of the formal scheme of A nth modules and I can So here the et al et sat al is the special fiber of the formal scheme? Yes. And the left is the rigid part? Yes. Yeah. So we also get a map phi which goes from phi upper star of this complex to itself. And if you sort of understand how L eta works, essentially when you do apply phi upper star with L eta it basically commutes except the commutations off by an element here. Instead of doing L eta mu you do L eta phi of mu. And so therefore the cononical map is going to have a kernel and which are killed by phi of mu divided by mu which showed up over there. So this is this map. So it's an isomorphism outside the kernel of theta. And that's just a completely formal calculation based on the fact that phi of mu divided by mu generates the kernel of theta. The point is that L eta doesn't quite do the phi star can you say that? Is it something really fast? I said if you do L eta sub little mu of phi upper star that's the same as No. Let's see. Hello. I think L eta sub if you do it in this direction then that's the same as doing L eta phi of mu phi upper star. Just because phi is an isomorphism so I'm just transport of structure. And so yeah. So in fact by the similar formal argument you can actually prove the following. So we have this we produce this map phi upper star A omega x prime to A omega x prime. And on the other hand you also have a cononical map here from L eta with respect to this kernel XE which was phi of mu divided by mu to A omega x prime just because this was a sub complex of things satisfying certain divisibility properties and there's a cononical isomorphism like this. And so this tells you in a precise sense how far this map is from being an isomorphism namely is the highest power XE you need to make this map an isomorphism and that's determined by the number of non-zero homology groups. So this is the morphism is on the one in the capital this isomorphism is just phi I think. Yeah it's the way phi works with L eta so that should be if Fabian is here. But it's completely formal based on how L eta works. Yeah so it's in the essentially. Oh sorry you're saying it's in the book. Oh okay. Excellent. The main thing is that we will get it actually. The L eta and the phi. Right. But I guess in their case well phi of p is p so yes thank you. Okay I lost track of which board I was. Okay. Right so this is the almost correct construction and this is almost correct in the sense that this is almost isomorphic to what we want and to get something that's honestly isomorphic we have to fix this almost non-sense. So I haven't actually done any almost mathematics but what is really going on is that this is living in the almost well you can think of it as living in the almost world and you modify it by something supported on the special fiber to make it correct. Is it clear why you needed to kill the torsion? What's the purpose of the L eta? Why did you put it in? So if you try to compute nearby cycles in this framework of perfective spaces say there's just a lot of bad torsion that shows up when you compute these nearby cycles you use. So for example if you did it instead of a nth just for the structure sheaf over here the torsion would be sort of really like infinite but the observation is simply that whatever that infinite torsion is is actually killed by epsilon p-1 and so when you do this L eta it just goes away. Okay and then the second step is you fix the almost non-sense so step two so I mean the way you do sort of you have something in the almost world and you want to get something in the real world the way you do it is that you modify it by something that lives in the quotient of your ring by the ideal of almost mathematics so in order to do that you're going to do the following so you're going to construct a net well I'm just saying you can do this so you construct a natural map which goes from the Diron-Witt complex of the special fiber thought of as a complex on the formal scheme to this complex A omega x prime scale are extended to W so the ideal of almost mathematics is the ideal cutting out spec W inside spec A and so all I'm going to do is I'm going to restrict to this slice and modify it by this map so let's call this map alpha and I'm not going to say anything about the construction of this map but once you've constructed this map you can sort of define A omega x as the homotopy limit of the fiber product of the following so here you have A omega x here you prime here's A omega x prime tends to W this is sort of the quotient in the special fiber and then here's the Diron-Witt complex and I'm out of time so I guess step three is that you check that this works ah what? it's 5 minutes ah 5 minutes is it an almost iso this map which map? the natural map some map is almost iso this one I'm not sure it's related to what we were discussing earlier so if I guess, no I don't know I would like it to be and I would simplify some of the constructions but I don't know if it's an almost isomorphism is that right? wait sorry which one? this one? ah no no alpha it doesn't make sense to talk about almost isomorphisms because it's taking place over W yeah sorry there's a version of this over W of O C where it doesn't make sense I got confused yeah no so maybe I should so we're really doing almost mathematics with respect to this closed immersion which is whose ideal as I said earlier it's cut out by p underline and all of its p power roots and then you also have to worry about piatic completions and then what I'm saying is that once you want to specify something over here you first specify something in the almost world which is a omega x prime and then specify what happens when you restrict to the special fiber and the way you specify what happens when you restrict to the special fiber is that you're allowed to arbitrarily modify it in this way okay and I guess I can write step 3 over here which is kind of stupid but it's where all the hard work happens so check all the specializations and so maybe I'll just say which ones use what so to use that the etal specialization is correct to use Scholes's theorem which is some version of Falking's theorem comparing X plus comology with etal comology and then the other two you check by hand so crystalline is more or less by construction so the crystalline specialization is what happens when you restrict to W and the way I'm modifying it I'm forcing it to look like the derambe complex so this is by construction and then the derambe one you'd really have to check sorry? so it follows from the fact that the specialization along the kernel of C gives you the derambe complex which is a perfect complex and so I guess I should have said this but you also had to theoretically complete everywhere so everything is complete along kernel of theta and then when you specialize along theta you get a perfect complex and so it's a perfect complex okay so that's all I wanted to say thank you there are some comparisons between the etal and etal comology from this picture sorry can you derive the comparison theorems from the crystalline and etal comology from your picture in this picture but in the same way that it's sort of I don't think the proof you get would be any different from the one that you get by faulting this machinery I have two questions first one, classical story in Bertrand August the generation on the special of Hartree-Gerrand E1 and the special fiber that's an important quote together with torsion's finesse of etal comology to get a nice representation and it doesn't appear in this sort of in Bertrand you discussed torsion's finesse in Gerrand but they didn't discuss the generation so is it important or are you talking about not the personal so there is a new general meta-august object you see which is really major still but then you get that the for example the Hartree-Gerrand with the special fiber abstract the Hartree-Gerrand the filtration under these conditions not the generation that you want plus torsion's finesse so I wonder if there is some analog I don't know the story so I can't really comment on it but what I want to say is that in chapter 8 you mentioned I'm getting old the only thing I want to mention is that if the crystalline comology is torsion free then each comology group is in fact finite free so you really have a lot of things you can do with it so anyway my second question after this question maybe related to the previous one so is there any relations between this a omega dot x and the complexes constructed by Sasha a natural a natural derangue a natural craze you give the I don't think so I think the complexes constructed in the H-localization picture are what you'd get if you did not do this modification at the end so like if you do our gamma of a script A derangue then you would have this Sasha's then here there's no such a thing I mean some of the comparison theorem is hidden formula similar so there should be some relation between two objects so I guess maybe one thing I can say which is related but not an answer to your question is that you can ask if there's a way to construct this comology theory using the H-localization picture and I currently do not know the answer to this although I suspect the answer is yes if you use topological H-cell homology but this construction won't work because it's a local construction okay so yeah why do you get an almost isomorphism between a omega x and a omega dish x you set it oh is this because the way I'm modifying it I'm modifying it by something that's almost zero so this side is almost zero so when you pass back to the almost world you just get a nice like any module over w is declared to be almost zero okay yeah probably probably I don't know but I mean I would strongly suspect yes okay so I have two questions maybe I will ask only one and then the other one right now so yes can you recall also the integral that we had you see when so look at the h i with i is less than minus one it should be so what you do get is that so this map this Frobenius map specializes to the comparison isomorphism and it's an it's invertible up to this element c so if your numbers if the dimension is small enough then you get some mileage out of it like so for example faultings has these theorems that say the integrally the comparison maps you constructs are always invertible up to beta to the d and that's this fact that this map is invertible up to c to the d up to c to the d where d is the dimension of x and in particular for more of the groups can you get c to the i or something like this that should be a formal question about this gauge construction and I can't think right now but I would guess yes