Okay, so I wasn't in the process of speaking about the total homology of diamonds. So let's try to remind ourselves a little bit where we are. So we were always working with this test category, it's called PERF, which was the category of perfectoid spaces of characteristic P. And this had two topologies, it has a pro etal topology, which was generated by open covers and co-filtered inverse limits, surjective etal maps of phenolites. And then there was another topology called the V-topology, where we allowed many more covers, so again that's generated by open covers and all surjective maps of phenolites. Okay, and then let me bring this back on the board, we had the definition that a diamond is a quotient, is a pro etal sheaf on PERF, it's called y actually, such that y can be written as x mod r, where x is a perfectoid space, or the sheaf represented by a perfectoid space, and r in x times x is a pro etal treatment solution. And there was a theorem that all diamonds are V-sheafs, and in fact many things generalize to all, and maybe there's a saturated condition of being small V-sheafs. And so in particular x is a small V-sheaf and r, so lambda again will be a ring, a coefficient ring, such that, and last time I was making some comments about statements which are true more generally, but at least from today on everything that is new today it will really be necessary to assume that n lambda is zero for some n which is not divisible by p. So if x is such a small V-sheafs then we have the drives category of lambda modules on x, by which I mean you take the V-side of x, which is just all small V-sheafs mapping to x, I mean ignoring saturated issues, and I'm looking at lambda modules on z, it takes the drive category of z. And in there there was a certain subcategory that I called d etal x lambda, which is essentially characterized by the properties that whenever I pull back to a perfectoid space it comes from the etal drive, I mean, okay let me first write this and then say what's true. So the thing to know about these categories is that containment in the subcategories can be checked locally and if x is a perfectoid space respectively n totally strictly totally disconnected, so strictly totally disconnected guys were these things which were essentially just profaned sets of points, and we were using often that anything can be covered by profaned set of points, then this d plus et was just the d plus of the etal side of x which can then be defined lambda, and if you want the statement to be true for the unbounded category you need this extra assumption. You can get in slightly more general settings if there is some bound on the chromological dimension. And in the strictly totally disconnected there isn't bound on the chromological dimension or not? Yes, it's bound on the chromological dimension zero, like for anything which is, any separated etal for the compact maps say to a strictly totally disconnected guys against strictly totally disconnected, and if you have something strictly totally disconnected then there is no higher chromology at all. Right, but there is a basis for the topology. So these are the objects we care about and actually the one we care most about is this guy. Okay, so let's talk about the six operations. So let me start with some simple ones. So first of all there is some tensor product, well that's a priori maybe defined dx lambda, just the usual thing we always have, and it respects this d et until you get it there. Let me say what I do for the r-home. If you take this, then this does not respect this guy. But you can somehow reflect it back, so this inclusion has an adjoint, which in some cases if you're a perfectoid space and line the d plus or so, you can sometimes more explicitly say what this really means. So this is actually a little bit tricky to understand what this means. Is it a left or right adjoint? It is a right adjoint. So this inclusion preserves all co-limits and then while you can upgrade the whole situation to infinity categories and then it follows from Lewis infinity categorical joint function theorem that there must be an adjoint. So if f from y to x is a map of small b-shefs, then the pullback preserves the d-ed. It commutes with tensor products. And so you also want to push forward. If f is q c q s, then the r-f lower star from dy lambda to dx lambda, it respects the d plus eta. It induces such a map. And under an assumption of bounded homological dimension, also on the unbounded derived category. I don't really find such an operation r-f lower star for q c q s morphisms, but I wanted this such an operation more generally. So for a general f, I can define the operation on this unbounded italic derived category as a right adjoint of f upper star. The homological dimension is for the r-f lower star or for both x and y? No for r-f lower star. So I think it's literally enough to assume that whenever you have an italic sheaf on y, then if I apply this r-f lower star, then r-f lower star is equal to 0 for sufficiently large i. So then there is this caution that this is not compatible. So equivalently, you can also embed the derived category for y into this four derived category of these sheaves. Then there is an r-f, let's call it b lower star, defined on the level of sites here. But this may not end in this d-ad, and then you can just reflect back. In f with qcqs, I recover it on the d plus eta and unbounded homological dimension also on the d8 in the form. So in the case of overlap, it's the same thing, but in more general cases, that is the operation I want to consider. So this takes care of four of the operations. And then there are two more, r-f lower star and r-f upper star. And at the end of the last lecture, I discussed a little bit the push forward with compact supports. And so let's remind ourselves about this. So for this, I need to talk about compactifications again. So let's remind ourselves how this went. So there was this funny thing that for edict spaces, there is this canonical compactifications. It's canonical compactification, which is somewhat slightly weird, which only adds a few higher rank points. If f from y to x is a separated map, then I can do the compactification of f over x. This goes from a space called y bar over x to x, which is given by the functor, which takes some spar r plus. And in some sense, forgets the information of cr plus, or at least it forgets all the information of r plus as regards y, but keeps it for x, as we still want something which lives over x. So it's the thing which maps this to the y of r, r-circ, where your points, sorry, sorry. So for example, if you want to map a, but I need to assume that this is totally disconnected. If you want to map some point, k, k plus to it, then you only need to map the rank one point, the maximal generalization to y, and maybe the full point, the higher rank point to x. So these kinds of single parametrize here, they are actually some of the kind of diagrams you would draw on the evaluative criterion of properties. And so we have this thing, and then f is compactifiable, f is separated. And so there's always a total, a natural map from J, an injective map into this compactification. And you ask that this is an open version. So let's just briefly discuss one example again. So if you have y, which is the edict spectrum of this guy mapping to x, which is spar k, okay. So this is a ball, a closed unit disk, but it's not quite closed as an edict space. It's not yet proper. And so you include one higher rank point. So then y bar over here is this thing, and then I take all k plus the maximal ideal. On the other hand, if y is the a1 over k as an edict space mapping to x, which is the first example, second example, if you have this guy, then actually y bar over x is just equal to y. And so this sounds strange, because you wouldn't think that the a1 should be proper. You would want to compactify it into a p1 maybe, but that's not what happens. And the reason is that actually if you consider the a1 as an edict space, then it's this increasing union of larger and larger disks, it's the union of increasing disks. And the kind of universal competition of each disk sits inside the next disk. And so it's what's called partially proper. Let's see the compact supported commodity of a1 you want it to be. Yes, that's why there will be a quasi-competitive condition in a second, okay. So you can, let's see how we define competitive support commodity. Partially proper is the same as this compactification, can we add anything? Right, partially proper is actually, well there's a more geometric definition for edict spaces, but one way to say it in our set up is that this map j is just an isomorphism. So it's a clue to saying that you have some kind of variative criterion. That whenever you have map from spa rr, cirk to y, and one, you draw such a diagram and then there's a unique map here. It's related to this one statement, this one variative criterion of properness that I stated last time. Okay, so this brings us to the following definition slash zero. So let's assume that f from y to x is a quasi-compact. So this, this allows this a1 example here for the moment. Because this is an increasing union of discs, quasi-compact morphism of v-shefs, small v-shefs, sorry, compactive phi bar, I need to add. Okay, so then we are in the situation where we have y, which embeds y and j into this compactification, which sits over x, this is f. And so then this map is actually open by assumption. And this map is proper, according to the definition of properness I gave last time. And so then if I look at rf lower shriek, which I defined to be the usual thing, you push forward after you extend by zero. So this is a map from dy lambda to dx lambda. This preserves the d plus eta, this induces. And also a map on the full derived categories. If rf lower shriek has bounded homological dimension. And it's compatible with base composition and base change. So a composite of compactifiable morphisms is again compactifiable as is a base change. Put them how the formation of y bar is smashed x is how strictly compacted with composition. Okay, so let me explain what happens. So if I z to y to x, then this has a compactification over x. This has a compactification over y. Yeah, and then this also has a compactification over x.  So it induces me just by restriction without any adjoint. Right, right, right, right, I mean. So it really, if you apply this to something that's d plus eta, it really maps, it applies this function, it really lies in the subcategory. One funny thing about the situation is that you could already ask this compatibility with composition without passing to the d eta. Let me actually write this down and then I believe it's not true. So there are very two remarks about this, which are related. So, well, no, maybe this one, so we could ask. So let's consider the situation z to y to x, f and g, f, g as above. So quasi-compact, compactifiable. Then you could ask the question, is if I first apply g and the f, is it the same thing as this thing on the full, guys? Okay, and I should one day sit down and actually find a counter example to this, but I believe it's not true. And so you actually need to restrict to this d eta to make this true. So there is a natural map in one direction, which I'm not able to figure out right now. And well, you can show that this is an equivalent. If you plug in such a guy, such a d eta guy in this eta thing, but it might fail in general. And so for this reason, it's actually net, that's the main reason that it's necessary to really work with this d eta and not something more general. There is a map in one direction. There's a map in one direction, yes. And on d plus also it should fail. Yeah, even on d plus, yeah. And I think even on this, there was this other guy that I didn't recall this time. So yeah, I think even on this kind of direction. Okay, so this way we get this R of law streak. Okay, then there is another unrelated remark. So there's another thing if this map is not quasi-compact. So then we can do the following. So if f is compactifiable, maybe not quasi-compact. But it is representable in locally spatial diamonds, meaning that all x prime f into x, where x prime is a locally spatial diamond, y times x, x prime is a locally spatial diamond. Then one can define R of law streak as a direct limit. And that may allow to be a little bit work here. Of all u and y, which are quasi-compact open, quasi-compact over x, say if the base is locally spatial, in general by descent. Okay, so the logic is a little intricate here. I just want to say you can extend it. And the essential thing is that you just defined as a direct limit of the lower streak for open subsets, quasi-compact open subsets, and then take a direct limit. This only works if you have enough quasi-compact open subsets. This is this condition of being locally spatial essentially. And so if everything inside y and x were such locally spatial diamonds, and this formula I would have written would be okay. In general, it's enough to assume that the map is somehow locally spatial. In which case, you just reduce to the previous case by descent. It's not the most critical thing. So this gives us five of the six functors and we need to find the last one. There's also a projection formula, let's say it's a quasi-compact compactifiable. A small v-sheafs then, R of law streak of. Yeah, so once you have the projection formula, you can essentially form it in space change terms. You can essentially formally get a knitted formula. Okay, so of course the last factor, R of upper streak wants to be defined as the right adjoint to R of lower streak. But to make this work, you really need to be in the setup where R of lower streak is defined on the full derived category. And so we have this assumption there of bounded homological dimension. And so I actually want to talk a little bit about dimensions for this reason. So this is holding on the what, or which A and B? Sorry, A, B are in the D, so A is in D et al. Y lambda B is in D et al, X lambda, sorry. And I might have to assume some bounded homological dimension again. Where is this? Okay, so it holds for this under if something happens that I didn't define yet. If some, sorry, if some dimension of S is finite, which brings me to dimensions. It's some kind of transcendence degree dimension, geometric trend. So this G stands for geometric, this trit stands for transcendence degree, and this dims stands for the mentioned. We will come to it. I'm sorry, maybe I was assuming for this one other little thing. Yeah, representable. Well, I can remove this and say it's representable in locally spatial diamonds. And the tricky thing with the projection formula is that this R of lower streak is usually better defined on the D plus, whereas this derived transfer product goes very unbounded to the left and you have to be a little careful a bit. I need to talk about dimensions. So there are the following notions of dimensions. So the first thing we need is a cruel dimension. If X is a locally spectral space, then it's a cruel dimension. It's a supremum of all n such that there exists a chain of specializations. X naught, X1. Whereas specialization means that one is contained in the closure of the other. Put this here. If f from Y to X is a map, is a spectral map of locally spectral spaces. I guess in principle one could, well, no, let's assume that locally spectral spaces. Then I define the dimension of f to be the supremum of the dimensions. Now, by the way, why does this live? This is either a non-negative integer. It could be infinite, but it could also be minus infinite. That's if f X is empty. The dimension of f is the supremum over all X and X of the dimension. And again, this is either a non-negative integer or infinite or minus infinite. But this only happens if y is empty. Are there notions of dimension functions? Are there notions of dimension functions? Well, so far we're here in the completely abstract setup. One could ask this for diamonds. Not really, I'm afraid. So there is this issue that the local, the usual closed immersion that one would want to look at, like a point mapping into a closed unit disk. They're actually not so well behaved in some ways in this world of hectic spaces because the complement of this map is a non-quasi-compact open subset, which means that this map has a non-constructible image, which means, say, that the skyscraper sheath supported at this point is not constructible. It also related to the fact that there is no specialization of a point of the complement into this closed point, as you know for schemes. And so actually, if you want to define the core dimension of this point, you can't really define it directly on the spectral space because the spectral space actually doesn't see that there is any, that they are connected in any way, really. It's a bit tricky. All right, so anyway, I mean, these notions exist. And then there is another thing that I need. Let's assume we have K contained in L, an extension of complete non-accommodian fields. Then I define the kind of continuous transcendence degree. There might be a C. So these names are essentially due to Huber of the Stimtre of L over K to be the minimum of the set of all N such that exists some L prime and L, a dense subfield containing K such that the transcendence degree of L over K, L prime over K is equal to N. It's difficult to get your other coefficients because you get only one. Right, so this is actually a slightly tricky definition. So there's the following very basic questions that I don't know the answer to. So I mean, what is true is that, okay, let me make a remark. So if K is contained in L, is contained in M, then there is a sub-editivity. This transcendence degree for M over K is at most the sum of the transcendence degree here plus a transcendence degree, this continuous transcendence degree. Sorry, I didn't want to call this, sorry. I wanted to call this this continuous transcendence degree, sorry. And then when I go to morphisms, I want to call it the dimension of the morphism, but sorry. Okay, so this is not so hard to see. But, additivity may fail, equality may fail, and equality may fail for good reasons. Say if K is something like this guy, so some complete algebraic closed field of characteristic P. And M is algebraically closed, and of transcendence of this transcendence degree equal to 1. Then there exist some, so you would think that I mean algebraic geometry, or for usual fields if you have two algebraically closed fields, one is of transcendence degree one over the other. Then there are no algebraically closed fields in between them. But this fails in this setting, so then there exists some K contained in L contained in M. Both proper, where L is again algebraically closed and transcendence degree equal to 1. Well, over K, but then I thought theory also for M over L. I mean if this was less than one, namely zero, then this would mean that there is a dense subfield which is algebraic over the base. But if this is already algebraically closed, there can't be further algebraic elements. Thus, this would have to be dense. But if these are both complete, then this would have to be in equality. But it's not in equality, and so this has to be actually equal to 1. Can it be also in characteristic zero? I think this can't happen in characteristic zero. So there's a paper of Matignon and Reversa, which discusses this problem. One funny thing to note about this paper from Matignon and Reversa, which is, I think, from the 80s, early 80s, is that they already find the notion of a perfectoid field in this paper. They called it a hyper-perfect field, hm? Science has progressed. So, additivity may fail. You could at least ask whether there's some monotonicity. And even this I don't know, yeah? Question, if you have the situation k contained in L contained in M, is it true that this continuous transcendence degree for L over k is at least bounded by the 1? Let me just note that the similar question for M over L is actually true. It follows immediately from the definition. But for this thing, it's not so clear because here you would have some dense subfield of M, which has some small transcendence degree. But this dense subfield has no reason to intersect L in any way. So it's not clear how to find a dense subfield of L. So, even in the case where M is the algebraic closure of L, I don't know this. So, in the absence of knowledge of this, of the answer, I define a slightly different notion. It's called geometric, to be what you get for the corresponding extension of algebraic closed-complete fields. And you can eliminate for k this operation? You can eliminate for k, I mean, it's the same as, and it's always less or equal to the 1 for L. That's by sub-additivity. It's less or equal to this plus the corresponding thing for the algebraic closure over L, but it is transcendence degree 0. All right, this is all stupid, but... I mean, I think it's an interesting question just in general to try to establish some good series of transcendence degree for these non-accompanient fields and see what properties what can establish and which fail. So, for example, this counter example is also interesting. Is the problem with this monotonicity? No, even then I can't answer monotonicity. But the problem I have is that if I have a diamond, then it doesn't have a val-defined residue field because it has a val-defined algebraic closure of its residue field. And so, I need a notion of this transcendence degree which only depends on the algebraic closure. So, here's a basic proposition. Let's say that. Let's assume you have a quasi-separated diamond, such that the underlying topological space is a point. So, what are the diamonds with a small quasi-separation? Whose topological space is just a point? We can understand those. Namely, then x is of the form spa COC, modularity action of G, for some unique but up to non-unique isomorphism as usual, complete algebraically closed field C, with a continuous and faithful action of a profiled group G. So, you would like to think of C as the algebraically closed residue field, the completion of the algebraic closure of the residue field. And as G is the Galois group of this point, but G may not be the Galois group of any actual field, it's just something which acts. Conversely, whenever you have such data of such a complete algebraically closed field C of characteristic P, with such a continuous and faithful action of a profiled group G, you can define such a quasi-separated diamond here, whose space is a point. So, you can understand the structure of points of attic spaces. And so I can make the following definition. So, in general, the field of invariance can be very small? The field of invariance might just be Fp or something like this. So, you might have the case that if you take spa Qp and then take its diamond, then what you get is somehow this field moduloos the Galois group of Qp, but if you take the invariance in here, you just get Fp. And so there's not any actual field in the business here. Anyway, so before the break, let me finish by giving this kind of transcendence degree dimension. So, let's say that f from y to x, let's say it's a map of locally special diamonds, this G stands for geometric, this T stands for transcendence, dim stands for dimension, of course, is the supremum overall y mapping to x of this kind of geometric transcendence degree. Well, which is actually the same thing as this continuous guy because I'm doing algebraic closed skies here. So, let's say that this is the sum of c of y over c of x. And I can add some maximal points where, well, I mean, it's equal to the true because we're only doing geometric guys. I just want to stress that even in the case where these work perfected spaces, I'm actually doing something different by passing to this algebraic closed skies where, say, if I, this is the localization of x at x and similarly for the definition of c of y. And c of x is defined up to isomorphism, but I mean, I'm only computing numbers and these numbers are in the end independent. The map of c of x to c of y is still well defined up to actions of some groups. Right. They don't change the, okay. Okay, let's have a break now for 15 minutes. Well, the localization of a spectral, in general, if you have a spectral space and you have a point in it, then there's the notion of the localization of the spectral space at this point which is just a set of all generalizations of this point. But if you have a maximal point, then there are no further generalizations. Well, I mean, if you would want to define such a complete residue field as a non-maximal point, they would be the same as at the maximal generalization. And so it's not really, not much is lost by assuming this is a maximal, just not with. Okay, so another basic proposition is that, so before the break, I defined this notion of this transcendence dimension for morphism. And the basic fact is that the dimension of f considered just as a map of spectral spaces is bounded by this geometric transcendence dimension. Now, let me just sketch it. So if x is a maximal point, if you look at the closure of x, then there's always embeds into the terrisky Riemann space for... What did you define as dmf? Ah, the dm of the fibers. What? I'm trying to concentrate here, okay? Always in terrisky Riemann space where a copper of x is, you take the residue field of C of x, it's completed residue field, and then actually there you can take the GX invariance and get a reasonable field because there the action is actually... Continuous for the discrete topology and then you're in a better shape. Sorry, if x is a maximal point and say, let's assume for the moment that x is separated. So there is a relation between the specializations of points you see here and the terrisky Riemann space of some fields. And so this bounds essentially the dimension, in this case maybe of x by the dimension of these residue fields. And so that's how you get this. So this bounds the cold dimension in terms of the transcendence degree. And this is some kind of relative version of this observation. Okay, so we have this. And then another proposition is the following. Let's say that x is a spatial diamond and f is a sheaf on its et al. side. Then the et al. homology of f is zero for any i which is larger than the dimension of x but the supreme overall x and x maximal of the homological dimension. Oh, sorry. Let's assume it's an L torsion sheaf. L not equal to p. Well, I think it's not even necessary. The L homological dimension of gx. Okay, so you can balance the homological dimension of the et al. side in terms of just the cruel dimension and the somehow galvanic homological dimension of these points. Let me sketch this. Let's look at the map from the et al. side to the just the side of the underlying topological space. Let's call this lambda. Then it comes down to two things. The first checks that if you push forward f under this map then this is zero for i bigger than the supremum over the L homological dimensions of these points. For this you just observe that the fibers are given by gx homology at least at maximal points, at non-maximal points you need a small extra argument but it works. On the other hand, the homological dimension of x as a topological space is bounded by the dimension of x. This is actually a theorem of Scheiderer from 1992. This holds for any spectral space. Of course, everybody knows the theorem of Grotendieg that if you have such an Assyrian topological space then the homological dimension is bounded by the cruel dimension. But actually, there's an unnecessary Assyrian hypothesis so this is always true. These are the ingredients. This tells us why the cruel dimension is relevant to the picture but now we need to unbalance the homological dimensions of these residue fields here. For this, business of transcendence degrees will be important. Let's say we're in the following situation. It's a spatial diamond over some sparse COC. By f, I want to denote this map from x to sparse COC. If I look at the supremum over all x and x of the homological dimension of this profile group gx then it's bounded by this geometric transcendence degree dimension if L is not equal to p. This relates, let me say what this comes down to. The sketch we'd use is to c' over c as some other algebraic closed complete field and g is a profile group acting continuously and facefully on c' but over c. This trivial action on c. Then we need to bound the homological dimension of g which wants to be this Gaoua group by the transcendence degree of c' over c. Of course such a bound is well known if g was an actual Gaoua group of a field over c but this is just some profile group which apparently has nothing to do with any field but you can still make enough of Gaoua theory work. It was well known Gaoua theory if g were a Gaoua group. In this case you wouldn't need an assumption on air. It might be true that this is also true if L is equal to p but I don't know what to prove this. What turns out to be true is that up to some pro-p group you can essentially control what g can be. You can still define some p and i and then g. There is some kind of inertia where this is pro-p. This quotient i and p are bound by Gaoua groups. C' and c have non-acquaintance fields so they have Gaoua groups in the real numbers. This one for c' might be bigger than for c and this is bounded in terms of the difference you see on value groups. This is bounded by the transcendence degree of residue fields. There is a general theorem in Bob Ike that relates the transcendence degree of residue fields as the value groups and the transcendence degrees of the fields themselves. You finish using this inequality. I don't see any way of controlling what this Waldian inertia here looks like. It might be really wild. It's wrong for L equal to p because it will look like Delphan-Fuchs-Gormulge of the algebra vector fields. This is a zero-critistic analogy. This can act on such a non-acquaintance field. It should be more of the same. Maybe we can discuss this afterwards. Finally, I must state what all of this discussion is leading to. Let's say f from y to x is a compactifiable map of small v-shefs, which is representable on locally special diamonds. By the way, this discussion also tells you why I'm making two assumptions throughout. One is that I assume that my diamonds are spatial, so that the underlying topological space is spectral, so that I can apply this theorem of Scheiderer bounding the conmodical dimension. The other is that I assume that they are diamonds, which was this condition about points. This condition about points comes up somehow through this proposition that if you have these maps from algebraically closed fields into them, which are pro-Ital, then you can control what these points look like. That's why this notion of a locally special diamond is really the setup I want to work in. Alright, so then, if a is then d less or equal to n, while lambda are a floor strip of a, i is then d less or equal to n plus three times. You would expect two there. It might be true with two. My proof doesn't give it. Let me tell you why, what's the technical issue that makes the sphere appear. So if you have y to the x in the map of spatial diamonds, the compactifiable map of spatial diamonds, I do not know whether the compactification y bar over x is again spatial. So it is a diamond. But I don't know how to get enough quasi-compact open subsets of this guy. So it's not true that if I take a quasi-compact open subset of y and then compactify it, it will be a quasi-compact open subset of this compactification just because again the closure is automatically closed because you are taking some compactification. So there is no obvious way of producing any quasi-compact open subsets in here. And so this means that I cannot actually apply this kind of proposition there which applied to spatial diamonds to this compactification and then you need to work around this and then there is a workaround but I don't want to go into this. But in any case it shows that if your system trig of f is finite then R of Lore-Schrieg has finite common logical dimension.  Such that this thing is finite. Then finally we can define R of upper Schrieg from d x to y is a right adjoint of Lore-Schrieg which in this case is defined on the full derived category. And in some senses it's a theorem because implicitly claimed there is such a right adjoint. So why is there a right adjoint? You use that R of Lore-Schrieg commutes with all direct sums in particular infinite direct sums and the infinity categorical adjoint function theorem. For this you have to briefly update this function to a function of infinity category and then apply it. Can we use the classical construction to go to more resolutions? Can we use the classical construction to go to more resolutions? I never learned to go to more resolutions. Sorry. I would believe that if these things are actually locally spatial diamonds then this should be okay. I mean, somewhere you need to be in the setup where this guy I call d ad is actually the derived category of etal sheeps on something. I think to apply this to go to more things. No? I don't know. And so then I would need to make very strong assumptions on x not just relatively but somewhere absolutely and I don't want to put absolute restrictions on x. Okay, I don't know what you could do there. Replace x by a simplistic system of special... Yeah. Well, I think once you pass through the simplest thing, I mean, you're not so far from this thing. Anyway, it exists. Okay. And so, okay, that's purely abstract right now and so we want to make this function explicit in some cases and so in particular there should be some kind of smooth morphisms for which f r of upper shriek is essentially just given by pullback twisted by something and then you can wonder what's the right definition of smoothness in our case. But you can also not do it and just define comodical smoothness as being satisfies what you wanted to satisfy. So f, as in the definition, as in previous definition, is l comma not particularly smooth. As usual, l is not p. If the following happens and essentially you just want to say that this function is given by pullback twisted with some invertible thing but you need to say this not just for x but for x to be base change but actually it's slightly simplifying that you only have to verify this for strictly totally disconnected guys. So the condition is following. If y is x prime to x where x prime is strictly totally disconnected if I look at, let's call this map fx prime it's a map from y times x, x prime to x prime if shriek pullback under this map it's equivalent to some l tensor fl star is functions from d h r x prime so the condition is just that there isn't equivalence of functions where l is locally isomorphic to fl n which may depend on where you are locally. So that's like the minimal requirement that you would want to put on a smooth morphism so if you have a smooth morphism it should be any pullback should be smooth so in particular all these fx prime should be smooth and if they are smooth then it should be of this form it doesn't matter it's all the same for this question. So that's the minimal thing you would want and the good news is that if this minimal requirement is satisfied then a few good properties follow so if it's comatologically smooth so in this definition of comatological smoothness I only used fl coefficients but actually things improve from there so then for all l power torsion rings lambda it is true that rf upper shriek is equivalent to something I call df turns out or maybe say this more canonically there is always a natural map from this kind of gadget to this guy this function is from d at x lambda to d at y lambda so this natural map is then an equivalent note that this is also something that's even for if lambda is just fl it's not part of the definition sorry I only asked this after pullbacks to strictly totally disconnected bases but it's already true on the basin what else? and rf upper shriek lambda is italically isomorphic to lambda and degree n sum n and z and the formation of rf upper shriek can be used with any base change meaning if I have y to x here I have some x prime mapping to it and I have some y prime the fiber product let's call this f prime and I have some fg, some fg tilde here then there is a natural transformation of functors from g tilde upper star rf lower shriek rf upper shriek maps to rf prime upper shriek g upper star so in particular the dualizing complex can be used with any base change so let's call this guy here df in particular the dualizing complex for its map f prime is canonically isomorphic to the pullback of the dualizing complex for f note that this is also something that wasn't asked in the definition that this sheaf L which appears there in this local equivalence is actually compatible with any base change it follows from does it suffice to prove to check this on one subjective? yes so if the base is already strictly totally disconnected you might ask yourself whether it's enough to check this not just on x itself not after any base change and this is something I don't know so you still need to check it for all further base changes to bigger algebraic closed fields somehow can this n be made explosive? what is this n that appears there? good question I don't know so this n somehow gives you another weight so you would expect that for example n is even but I don't know this for the affine space it's just what you expect okay I will come to some examples in a second there is still some time left what was the question? what I wanted to say what is this n? so this n somehow gives you another way to define the dimension of the smooth morphism so it's the degree shift in the dualizing complex and I don't know how to relate this in general to the these other dimensions I was discussing so there is some fuzziness about dimensions right now in the theory that needs to be resolved but anyway so if you have such a comodically smooth morphism then the theorem essentially tells you that everything you would expect to be true in the usual formalism is true but this doesn't tell you that there are any examples so maybe let me just note this I mean so color is that you you get a smooth space change in punk radiality but this is completely abstract so we need examples well what's good about this notion of comodologically smooth morphism is that it has a lot of good stability properties so let me first note these stability properties so once you have some example you get a lot of other examples and then in the end I will tell you one example one base case so composites of comodologically smooth are there is a two out of three properties so if you have g from z to y f from y to x this is surjective and if g and the composite are all comodologically smooth then f is all comodologically smooth so you can check whether you are all comodologically smooth you can check this all comodologically locally then this comodologically smoothness is v local on the target it's the first point composites are and then there is a funny operation so assume we are in the following situation f from y to x is all comodologically smooth and g is some pro p group pro prime to l but let's say pro p acting freely on y over x with trivial action on x then if I take the quotient by k from y mod k to x then this is still comodologically smooth so we call that a lot of the examples were constructed by taking something more explicit and then quotienting out by some action of what's often a pro p group and so this takes care of these quotients by pro p groups if you take something smooth and quotient by pro p group it's still smooth and then there is this one example that gets everything running it's that if b is a v sheaf which takes which is some of the closed unit ball which takes r plus to r plus then the projection from b to the point is alcohol in other words if I take spalf I can base change this to some non-accommodient field and then it's just this usual closed disc and the end is two and so rf upper shriek of lambda isomorphic to lambda t twisted by one shifted by two okay so sketch well the hardest part the one where most input comes into is of course the last part and this uses pretty much everything from Hooper's book so it uses extensively so the essential thing you need is you need a complete series of prompter radiality where smooth curves over algebraically closed but this is this is done by Hooper one thing to note is that here it's really important how I phrase the definitions that I only need to check something over these strictly totally disconnected bases and then by some reduction arguments I can actually get rid of this profiled set and just actually work over a point and so in the end everything is just reduced to the classical setup of the ball over a point and then again directly to side Hooper's book great and so now starting with this one example and using all the stability properties you can now verify there's lots and lots of things that are logically smooth so for example you could take the a1 over cp it takes the associated diamond so then this lives of a spar cp diamond which is just the edge of the spectrum of the tilt how does one see that this is alcohol logically smooth so this can be checked locally so and this is an increasing union of balls so reduced to well you could say it's an increasing union of balls but you could also do something slightly different and you can essentially reduce to the case of a torus the first reduce to the ball but then this ball is covered by two copies of a torus t is the set of all the points are the set of all x which are absolutely really t of cp is the space but then you actually t is the spar of cp this guy and so as in the first lecture you have this t infinity where you join all p-par roots of it and then t infinity flat it's the same thing for the tilt and so this is actually open in the ball it's just the subset of points where the absolute value of t is equal to 1 and so this implies that ah maybe they should have also been a part 0 that etal implies alcohol logically smooth so this is alcohol logically smooth this is open in it and so t infinity flat mapping to spar cp flat alcohol logically smooth but then you can recover t as a quotient let me finish this sword but then if I look at this torus of a cp and it passes the diamond then this is t infinity at some point I lost the subscript cp the tilt modulates the action of cp everything here over and so now I use this funny statement 4 so you use this and then you conclude that this guy is alcohol logically smooth let's do another example this shows that in general smooth attic spaces are yeah so in general you can use this to show that smooth attic spaces are alcohol logically smooth because well because composites are and well the products are also alcohol logically smooth so you get that f i in spaces are alcohol logically smooth in general something smooth over an f i in space and then and then it's always twice that I mentioned and right so I wanted to do another example so at one point I had this guy beat around plus mod fill 2 which had this extension which was an extension between diamond a1 over cp so this is an extension of group diamonds I guess these examples are called pannachal mess spaces over sparse cp claim is it smooth sorry I mean maybe I should say more precisely what I mean so I have this beat around plus mod fill 2 well it is a diamond and this maps to sparse cp diamond and I claim that this map here and as this is really an example which doesn't come from usual geometry it doesn't it's not a smooth attic space or anything and so it's really non-trivial to get your hands on this guy is any group object alcohol logically smooth well all these pannachal mess spaces are alcohol logically smooth well any group object I'm not sure I can talk about any group object I don't know what they are no no that's it's true for any I just want to consider the simplest example to explain how the arguments go so this maps to the a1 over cp diamond and we know this is smooth by the previous example and so it's enough to prove that this map here is smooth it's enough that f is smooth but now we use that this can be checked locally we locally and we locally this has a splitting and so once you fix the splitting and so if you have a map space x mapping so ejectively onto here such that there's a splitting then this relatively this just decomposes as a product of x with this a1 which is comodically smooth by base change and so let me just finish by saying that for those who know what they are is that all Banach commas spaces are comodically smooth I mean all positive yeah I could be underline not okay so all connected Banach commas spaces effective as I called so of course you would really like to have a more geometric definition of what it means to be smooth but the problem is that what we're working with is in some sense something like a topological space and it's not a manifold so if you had a map of many folds you would know what it means to be smooth because you can look at tangent spaces but if you just have a topological space what does it mean for a map of topological spaces to be smooth and so I'm unable to give a direct geometric definition of this and so but so far one can work around this just by working with this very abstract notion of comodical smoothness that can then be verified in the example to care about and the pro etal map is that the pro etal map is not comodical smooth so ah so another property of comodical smooth maps is that there is some finiteness properties for their comology so they automatically if lower streak preserves constructable sheaves for some notion of constructability but in particular if you had a pro etal map say over a geometric point it might be something like a pro finite set but the comodgy of a pro finite set is of course very big so this is not allowed the question was whether pro etal maps are smooth comodical smooth and they are not and the essential reason is that ah you don't have finiteness of comodgy for them so something like a pro finite set mapping to a point is pro etal but the comodgy of the pro finite set is of course very big because say the h0 is already very big ok so there is no higher comodgy but the h0 is really big ah and so that's not allowed ah did I want to say anything I don't know question how about localisoclasticity localisoclasticity come tomorrow I will talk about localisoclasticity ok is there some general reason for saying that something is compactified is there some general reason for saying that something is compactifiable no but again like in these procedures here why you were having some examples and you were like the same kind of reduction procedures that you were doing here they also worked for the compactifiable notion so in practices it can be checked


Greetings from the Commonwealth of Learning, or CALL. CALL is an intergovernmental organization established by Commonwealth heads of government when they met in Vancouver in 1987. We are very privileged to be in beautiful British Columbia and thank our hosts, the Government of Canada, for making this possible. What does CALL do? Our mission is to help Commonwealth Member States and institutions to harness the potential of distance education and technologies for expanding access to education and training. I was happy to learn that you have chosen to focus on gender equality and youth in the Commonwealth, two themes that are very close to CALL's heart. We have a very young Commonwealth where 60% of the population is under the age of 30. And when I think of young people like you, technology and learning come to mind. Two keys that could open many other doors. Technology and knowledge are multiplying at a rapid pace, even in developing countries. The number of mobile subscriptions worldwide is approaching the number of people on Earth, which is almost 7 billion. Studies estimate that mobile penetration has reached 90% in developing countries. Internet usage has also increased and 40% of the world's population is now connected. Two-thirds of them are from the developing countries. As heads of government and foreign ministers, I know you will be making important recommendations in your communique on how to improve the situation of young people in the Commonwealth. Let me share with you three examples of CALL's work that might trigger off ideas that could help shape those recommendations. First, the low-cost and high ownership of mobile phones has provided CALL with an opportunity to engage many young people, especially women, in rural areas. Through CALL's lifelong learning for farmers program, rural women have used their basic mobile phones to learn and to access opportunities for livelihoods. Here is Valar Mati from India. She could not complete primary school, but learned the intricacies of financial management and goat husbandry using her mobile phone and she learned in her own language. Today, she is a business correspondent for a major commercial bank and makes enough money to support herself and to send her children to school. Second, CALL's APTIS or the Classroom Without Walls is a technology innovation that is reaching the unreached. It uses solar power and a wireless router, so you don't really need connectivity and yet it provides teachers and students access to good quality digital materials such as Wikipedia for schools and a whole library of free books and videos. This low-cost device has provided valuable learning opportunities to young people in rural areas without any internet access. In the aftermath of Cyclone PAM, which as you know devastated many Pacific islands, the Ministry of Education deployed APTIS to ensure that young people could continue to learn even when their schools were closed. Third, CALL has employed appropriate technologies to help youth develop technical and vocational skills. One partnership in Kenya led to the development of a construction and building course meant for young people. This is Eunice Maganga who was a participant of this course. She wanted to be a construction worker like her father and because of this training was able to contribute to her family income and pay for her college fees for further training. I hope these examples have demonstrated the ways in which the creative use of appropriate technologies can create learning opportunities for young people, particularly women and girls. More than ever before, youth in the Commonwealth will need to continue to learn, unlearn and relearn many different things during the course of their lives. You will need to be lifelong learners if you are to contribute to the sustainable development of your society. During your deliberations today, please consider the value that learning and technology can have for empowering women and youth in the Commonwealth. So your Excellencies, Commonwealth Heads of Government and Honorable Foreign Ministers, thank you for listening and good luck with your deliberations.


California Spangled Cat vs Bengal Cat. What are the differences between these two cat breeds? The California Spangled is a mixed breed cat A cross between the Angora, Siamese, American Shorthair, Abyssinian Manx, and British Shorthair breeds. The California Spangled was bred to resemble a wild cat. These felines are very athletic and can be energetic, but they also have a super loving and sociable side that makes them excellent family cats. Just make sure that you have a large home environment to satisfy their play and exercise needs, and also note that the mixed breed doesn't fair well being left alone for long periods of the day. The Bengal could never be called delicate. They're athletes, agile and graceful with a strong, muscular body, as befits a cat who looks as if they belong in the jungle. Despite their wild appearance, Bengal cats are actually quite affectionate with their human families. That said, they also have high energy and a fun loving playful side. They want to stay active and need a home that can match their energy. If you can fulfill Bengal's need for exercise, you'll have a smart, loving cat who can keep you on your toes. The California Spangled's coat can come in a range of colors which often include gold, brown, white, black and blue. They also sport their distinctive leopard style spots. When it comes to grooming, the California Spangled is a pretty low maintenance feline. Their short, spotted coat can be brushed once a week. Doing so will not only help ward off the chance of any mats forming but also keep the coat in clean and healthy condition. Regular brushing also lessens the chance of hairballs being an issue for the cat. When it comes to climate, the California Spangled is generally seen as an adaptable cat who can usually live happily in most climates. Just remember to always make sure adequate shade and fresh water are provided when the temperature spikes. The Bengal could never be called delicate. He is an athlete, agile and graceful with a strong, muscular body, as befits a cat who looks as if he belongs in the jungle. His broad head is a modified wedge shape, longer than it is wide, with rounded contours. A top it is medium-sized to small ears that are relatively short, set toward the side of the head. Large oval eyes are almost round. Joining the head to the body is a long, muscular neck. Supporting the body are medium-length legs, slightly longer in the back than in the front, with large round paws.  When a Bengal rolls over, you can see that another characteristic is a spotted belly. Enhancing the Bengal's wild appearance is a short, thick health that feels luxuriously soft and silky. It comes in several colors and patterns, including brown tabby, seal mink tabby, black silver tabby, and seal silver links point. The coat can be spotted randomly, or in horizontal patterns, or it can be marbled, with horizontal stripes arranged randomly on a lighter background. What exactly are you dealing with when you adopt a California Spangled? Well, first of all, you can be reassured that, while the mixed breed was developed to look like a wild cat, there's nothing predatory or wild about this feline. In fact, they are one of the most affectionate and loving cats around, so much so that, if you leave a California Spangled alone for too long, they may act out if they become stressed or become withdrawn if they start to feel lonely. Naturally, this is also a highly athletic mixed breed particularly known for their leaping and jumping feats. So make sure there are lots of opportunities for the cat to explore the homestead and climb to their heart's content. It goes without saying that a cat tower is essential for this mixed breed. The California Spangled also has a playful heart, so if you have young children, you'll find that the cat quickly becomes like a new best play buddy to your kids. The Bengal is highly active and highly intelligent. This makes him fun to live with, but he can sometimes be challenging. On the whole, the Bengal is a confident talkative, friendly cat who is always alert. Nothing escapes his notice. He likes to play games, including fetch, and he's always at learning tricks. His nimble paws are almost as good as hands, and it's a good thing he doesn't have opposable thumbs or he would probably rule the world. Board Bengal cats can also adopt some unconventional and slightly destructive habits, including turning light switches on and off. Fond of playing in the water, the Bengal is not above jumping into the tub or strolling into the shower with you. Aquarium and pond fish may be at risk from his clever paws. He also loves to climb and can often be found perching at the highest point he can reach in the home. A tall cat tree or two is a must for this feline, as are puzzle toys that will challenge his intelligence. On the rare occasions that he isn't swinging on chandeliers or swimming in your pool, the affectionate Bengal will be pleased to sit on your lap. It goes without saying that he will share your bed. And yes, he steals the covers. Hello. This video is sponsored by Beemix Pets. Are you looking for high quality cat collars at an affordable cost? Check out BeemixPets.com. Use coupon code KittenLife, to get 20% off. The California Spangled is always going to be ready and willing to embark on a play session or explore the highest parts of their environment. So, as a responsible guardian, you'll need to first make sure that their home is spacious enough and well equipped to satisfy the mixed breed's exercise needs. The short, thick coat of the Bengal is easily cared for with weekly combing to remove dead hair and distribute skin oils. A bath is rarely necessary. Brush the teeth to prevent periodontal disease. Daily dental hygiene is best, but weekly brushing is better than nothing. Trim the nails every couple of weeks. Wipe the corners of the eyes with a soft, damp cloth to remove any discharge. Use a separate area of the cloth for each eye so you don't run the risk of spreading any infection. Check the ears weekly. If they look dirty, wipe them out with a cotton ball or soft damp cloth moistened with a 50 to 50 mixture of cider vinegar and warm water. Avoid using cotton swabs, which can damage the interior of the ear. Keep the litter box spotlessly clean. Cats are very particular about bathroom hygiene, and a dirty box may cause them to start using other places in the house instead. It's a good idea to keep a California Spangled and Bengal as an indoor only cat to protect them from diseases spread by other cats, attacks by dogs or coyotes, and the other dangers that face cats who go outdoors, such as being hit by a car. Keeping them indoors also protects local birds and wild life from this avid hunter. If possible, build them a large outdoor enclosure where he can jump and climb safely. Cats who go outdoors also run the risk of being stolen by someone who would like to have such a beautiful cat without paying for it. The California Spangled is a perfect choice if you have children. Just be sure that early socialization takes place and boundaries are properly set on both sides, and supervise early interactions between kids and cats. When it comes to other household pets, the California Spangled is fine living alongside other domestic animals. Although you'll want to supervise early interactions between the new cat and existing pets, as well. Ultimately, early socialization really pays off with this mixed breed. Make sure to reward your California Spangled for good behavior when you bring them home to your family. The active and social Bengal is a perfect choice for families with children and cat friendly dogs. He will play fetch as well as any retriever, learns tricks easily, and loves the attention he receives from children who treat him politely and with respect.  Nothing scares him, certainly not dogs, and he will happily make friends with them if they don't give him any trouble. Always introduce any pets, even other cats slowly and in a controlled setting. Like many active cats, Bengals have a high prey drive and should not be trusted with smaller prey animals such as hamsters, smaller rabbits, and guinea pigs. If you enjoyed this video, kindly press the like button. Also don't forget to subscribe with notifications on, so that you don't miss out on videos like this. Thank you for watching.


Hey guys in this video, I'll be talking to Robert Cislow whose Grant Cardone's production manager And also in my mind one of the best video producers in the world and definitely one of the fastest The guy is an incredible inspiration and lives and breathes Grant Cardone Unfortunately in this 40 minute interview the first 20 minutes You don't see my face when I talk It was a some sort of glitch with the program, but the second 20 minutes about the 20 minute mark You're gonna see my face when I talk So I hope you can get by this small issue because the video is absolutely incredible You're going to learn a lot about how to produce how to actually get yourself No, and how to get attention what it's like working with the Grant Cardone And how to start taking action right now to get attention for you and your business and actually start growing your online Presence in the best possible way the guy has an amazing Insightful look into success and you're not gonna see that type of mentality that type of philosophy Anywhere else because this guy works for Grant Cardone works with him 24-7 for a couple of years now I admire him. I highly recommend you watch this video all the way through enjoy. Hey, Robert What's up, man? What's up, Robbie? How you doing, man? Good good Well guys Robert Yeah, no, but but my fans know that I'm usually up at these hours Because I make a video every three four days that I bitch about having to meditate at these hours Got it. Anyway, Robert is Probably the guy I want to be the most right now He's basically Grant Cardone's Video guy production guy Advertising guy the dude is a master at promotion and branding and Managed to hit income levels that most people don't even realize that you know people without a business of their own Could reach So he's a huge inspiration in many areas and I think that His content is extremely related to the fact that you guys want to make videos Because I don't really talk about the technical too much, but Robert is a master of basically how to make it right how to advertise right how to Brand yourself right and how to promote in the best way Well, thanks, man. I appreciate that took a lot takes a lot every day. I'm still learning every single day about it You know, there's always something new to figure out always something new to understand and yeah I mean it was interesting. You said the thing about the income levels When I started I was making What was I producing I was probably producing about 50 50,000 45 to 50,000 was like the baseline salary And working for Grant it really turned into this offer. Well, he's all sales and I didn't know anything about sales I was good at the creative part. I was good at making things look flashy and exciting really interesting and interested in documentary films and making things look pretty, but then it took a switch when There was an opportunity to start selling those services and I had never sold over the phone or reached out to people or Communicated that way So I just started picking up the phone and that was Grant's words. I'm like, I don't know what to say What do I say? What do I do? He's like just pick up the phone and start calling people and that's exactly what I did I got hung up on I got bitched at I got screamed at I got yelled at and then I had a few people that were like We love this dude. Let's do some business and then I closed my first deal the first deal. I closed the Contract value for the branding was 15,000 and I was super stoked about that I'm like once I got it and it came through they signed it. They send you the credit card information like dude I did it But you know now I think the biggest deal I've closed was probably 100 150,000 is the largest deal I've closed so far Well I'm I'm you know as as a coach and Many other people that listen to me are sort of the coach type or Maybe they have a business of their own, but they want to focus on the artistic side Sure the creative side.  I'm like, yeah, you know, let's make sure that works out Let's do that. It's a good relationship So how did that kind of change? When you started working with grant and how that affects your life Wow, that was that's a really good question because I was so focused on the artistic side of it And I believe that I was like man if I just make this one video Everybody's gonna come and find it. They're gonna want to do business with me. They're gonna love me It's gonna be great and I did that one video and nothing happened and then I did another one and nothing happened and I'm like Okay, what's happening here? But the the point of the matter is I Had to start to embrace the sales side. I didn't want to I was actually afraid to do it because I thought if I started Acting like a businessman as an artist. I would lose the creative side like that was my biggest fear I'm like, well if I put all this attention on the sales You know the processing the putting together the deal doing all that I would lose the ability to be an artist, but actually it enhanced It enhanced it it made it actually ten times more fun because I got to take the creative side of the video production and throw that into the craziness of a sales process and You know, that's how I went from making 50,000 to making 150 plus, you know, so it's like and I would say probably ten months and You know, it's To not embrace the sales thing and that's I think the biggest part about artists is that they get very caught up in the art They're very like I've done this beautiful piece of work And it's like you're broke you don't have any money like you can't what can you do? You can't you can't take that piece of art and ship it to somebody because you're worried about how you're gonna put food On the table later now. I'm not saying that to disparage or talk down artists It's just I think it's the piece that artists are missing is the actual sales portion Because it takes a lot of energy to reach out like I've had I think to close one deal I have to call a hundred and fifty people and actually have a hundred and fifty conversations To close one deal on why they should allow me to do production with them or branding or advertising or build a show and It takes tremendous amounts of energy to talk about the creative part because it's yeah I know I'm a good artist, but nobody else knows what that is So how do you relate that to somebody that doesn't know anything about you? So, you know, they'll be like, oh, yeah, he's the guy that does videos I'm yeah But do you know that there's like 12 tracks of music and 14 layers of effects and then all these little like you Don't know that because I don't tell you it Or the artist that paints it's the same idea Well, I use acrylic paint and then I use water paint and then I put the paint outside in the sun for three months And then I come back to it. You know, it's just processes that make it interesting And that's part of the sales thing grouping together the artist and the sales Together is what will actually make you successful. Yeah, I loved how you said That's the missing piece for the artist.  You know, so yeah, yeah, just a small tangent question I was doing 3d modeling like art You know characters Weapons stuff like that when I was 14 years old and I was one of the best people in the country because I was obsessed with it But then I realized that I can make money off of it And then I got greedy and I would only make art that would make money. So instead of asking like, what do I want to make I? Asked like what makes me money? And even today as a coach, I don't go for the clients that Would necessarily pay me just to do the kind of the process of coaching I go for the ones where I feel like the most creative the most You know fulfilled as both in the art aspect and as a business guy How do you kind of reconcile that where you you got the sales part down now so you can you know, you can sell You got the art part down So you know you're good at your craft But how do you make sure that you actually don't you know start going for the money too much? Where you work with clients that you maybe don't like you do projects you don't enjoy For cash Sure, sure. Well, I'm gonna go the complete opposite of you because I have a very different viewpoint on that and here's why I'm gonna explain to you why I used to be like that But at the end of the day for me, it's I do I am money focused I'm focused on that, but I'm also focused on helping somebody So for me if I know let's say like this is Joe and I don't like Joe, but I know Joe has money I know Joe has a service that he needs to promote I would feel better about myself to just kind of push that that that thing aside and be like Okay, I'm gonna do the job with Joe and get the job done because at the end of the day My survival is the most important thing My future is the most important thing being able to provide, you know Take care of the bills and everything that I need to do At one point you have to make a decision and just say Okay, it will be a pain in the ass to work with Joe I already know it would be a pain in the ass to work with Joe But if I work with Joe and I get the job done Joe is another satisfied customer that's gonna go tell a hundred other people about how good of a job that I did Even if I don't like Joe even if I think and I wouldn't say that, you know You don't want to say oh Joe you're an asshole because we all have people that we're just like man I don't know dude.  It has it's more about them your job is to help them That's it whatever if they start freaking out or if they have a bad attitude problem now if Joe is a drug dealer I'm not gonna do business with Joe. I do have some standards. I will be honest But if Joe is just kind of like kind of like an annoying person like you know, I would I would put that aside to help him out Yeah, I'm gonna bring back I'm going back to your video like I've seen so many commercials of you from my grand grand card on TV, right? Yeah, great for the TV from ganker down TV So many commercials. I'm imagining like do you like drugs? Are you a drug addict? That's actually one of the things that why we built the network was because we actually wanted control over those commercials We didn't want to have like, you know depressed anti-depressant medication or Viagra commercials or you know anything that was just Lower than being entrepreneurial being successful and being highly motivated So that's actually a part of the reason why we had the network Why Grant built it because he wanted a place where it was just informative without being interrupted by stuff like that So yeah, so I wouldn't do anything with big pharmaceutical companies. Yeah, but and also probably you Like it when you take control of the monetization Rather than you know have for example YouTube monetize for you You probably make a lot more money either way. So Yeah, I mean you have I mean control is income Grant talks about that all the time the more that you control a process the more that you Control something the greater your income is going to be Yeah, I loved I loved how you You kind of changed, you know my paradigm a bit When you talked earlier about, you know about Joe who needs help Like I didn't realize it, but you know how you said, okay, look you make money. You help somebody He introduces you to new people That might need your help also.  So I'm only going to work with those that Represent myself the best like right it's selfish. It's true. I had a guy I had a guy called him and he said to me He said I'm not interested in communicating anything about sales. Are you trying to sell me something right now? I'm gonna hang up the phone. I'm like listen sir. I'm not calling you to sell you anything I'm calling here from what your business And he switched and that's part of the sales thing, you know like Joe being a Guy who's very like reactive and very blah blah blah blah blah blah you just have to go in and this is this is where the artist doesn't really Go into it's just the art, but this is the sales side now Because now I have to like say okay. I know my art can help him But I need to cut through all of his stuff for him to understand that I'm trying to help him out You know to me does that make sense? Yeah. Yeah, absolutely. I mean I made a Probably over a thousand cold calls this year. Yeah And it was brutal.  Yeah It's brutal like it's hard for the ego It is brutal and that's why you are Yeah, I mean the more frequent that you do that the easier it is for you to withstand that kind of like it You know like you call somebody and they're like, I'm not interested It's like I know you're not interested. You don't even know what I'm talking to you about Of course, you wouldn't be interested and I take full responsibility for the fact that you're not interested But I'd like just because sir you are not interested That wouldn't stop you for at least being interested for 30 seconds for me to tell you how I can grow your social media by 1900% in 60 days what it and they'd be like, what you see It's it's and that one I just really started getting good at I watched Grant's mastering objections Webinar which was like the thing that I struggled with the most was how do I handle somebody objection? I was good at sales I was good at the clothes and then an objection would come up and I would just like bypass it go Like I would skip over it and I would just pretend I didn't hear it. Oh, yeah That's a very crucial part to have to handle and again like if an artist is trying to sell a $7,000 60-foot piece of work You know, they have to know how to handle that like they could call like the Hyatt Regency or the what is it? the JW Marriott or The Ritz Carlton and say I want to put this piece of art in your lobby.  What are you talking about? The artist needs to know how to handle that So the biggest the biggest thing for me between the artist and the sales process is that missing piece of actually understanding how to sell How to liquidate objections exactly pretty much. Oh, yeah, I mean, I remember first trying Grant Cardone's You know when he taught that like in seller be sold that you know, you take the Objection and you treat it as a complaint Like it made all the difference for like It is I would make like cold calls and they would be like I don't have time to talk to you I would be like, oh sure. I know so when will you be available and And then they're like I'm not interested. Of course now you don't know me.   Yeah, like yeah, exactly One yes, it feels good.  So now when somebody says it. I'm like You know, yeah, it makes you actually feel like you can control What goes on around you like you're not a slave to people's Opinions and statements so they could say this is the situation you flip it and you realize hey like it's it's liquid It's it's all subjective. You can change it Exactly So so just relating to the Again the selfish part. I have so many people that comment like hey, I'm opening a channel a YouTube channel because of you But then they they get stuck either because they feel like, you know, they don't really have what to say or or or more importantly because they don't understand the You know when I work with clients, it's different because I kind of guide them one-on-one. You know, it's really intimate but when I Make videos I can only help so much and then they you know They want to open the channel and they get the link they get like okay attention Equals money you make you get enough attention you get you'll get the money Or at least you can use it to get the money Right, but but they can't make that link like how do I like use a video and Make money like am I not supposed to get that from you know from a boss or from you know So so how would you say somebody who wants to start a channel or maybe just started?  I mean anyone. I don't have a business that I can't touch and help The key component of that because I ran into it is what do I say? After I do five videos, so I feel like I covered everything you know and and How to get past that is to really identify what is the purpose of what you're trying to do? So if the purpose is you have to think of social media and YouTube How do I put it as a as like a fishing line that goes out into the big ocean now? You know how large the ocean is so if you drop five videos I'm not making a dent in the ocean yet if I drop 300 videos I'm still not making a dent yet where you start to make a dent is where You bring up the level of consistency and the frequencies to which you drop content So what I'll do is is like you're recording this video. I'm recording this video I'm gonna drop this on my YouTube page then I'm gonna tape it and drop it on my Twitter Then I'm gonna drop it on my LinkedIn and then I'm gonna drop it on my Facebook page And then I'm gonna cycle that over and over and over again. So every piece of content that you have You know you tag it right you drop it right It's all based on these little subtopics of the part of the business that you're in so like you're a coach I would talk about every single thing that you do I'd interview clients. I'd ask client questions I'd put I would do something as simple as you know, I would do a 30-second video about you making a list about a contact clients all the stuff that you think is mundane and ridiculous Is something that somebody's gonna be interested in because you're coming you're becoming so transparent and Your name is becoming synonymous with the field you're in so like video Roberts is slow You know Robbie coaching like that needs to be the target of what you're doing every day So where do you begin? Look at this entire spread of everything you do and then make a video about it and then recycle the content over and over and over again like a machine awesome, awesome So this is probably not I'm gonna be some a question that people don't usually ask during interviews, but you know Probably a couple of hundred people are gonna see this everybody that sees this wants to be successful thinks about success Maybe tried and and fell, you know many times, you know, we're kind of start and then don't you know go through with it With the resources because again, you've been working with Grant Cardone for a couple of years now Again super gels With the resources you have available, you know the books the the production company the Grant Cardone TV everything like Let's say somebody funnels into Your content like where should he go? What should he do? What should he watch? Where do you begin? So much are you asking are you asking me about me specifically or if they're trying to do you and grant have so much content Mm-hmm so many products Mm-hmm so much information so many channels Mm-hmm Where would you recommend somebody to to start to go first to? Kind of start embracing the empire of content that you two built Good question, so you're gonna want to go to Grant Cardone TV comm and just start watching Grant's shows Like young hustlers and Cardone's own that'll start getting your mind right that'll start putting things together for me I'm pretty big on LinkedIn I've been writing a lot of articles lately about what it is that I do plus my YouTube channel plus Grant's YouTube channel Now as far as being successful You know how to how to be successful with the resources that I had available the number one thing that helped me the most was Grant's training platform Cardone University and I train on that every day and That allows me to get this in the right frame of mind Whether I'm going to be doing sales or whether I'm going to be doing promotion Like it puts me in a space where I can start to really identify You know what avenues I need to take in order to sell my product or service For me if you're wanting to learn about promotion and marketing and what I do Through Grant Cardone TV you can go to grant card on TV comm forward slash brand yourself and there You're gonna find a lot of information. I got a free e-book there. You can check that out I will actually probably personally reach out to you because that's I'm very responsive across all those platforms to Help identify what direction you want to go because success is dictated really on Clearing up the mind, you know really getting this added like literally you have to lose this in order to start be successful And Grant said that once he's like I lose my mind to become successful Like I don't know what you're talking about But now I know what he's talking about like there's so many things that come in when you're trying to build something You're like who's talking stop it so that what you need to do is really stay completely focused on Your direction your momentum what you're trying to build and then go to people that are doing it I would say that's the biggest thing like grants done it Grant is there I'm just basically modeling the whole production thing after what he did because I saw it be successful And I see success through it so for for anybody who's looking. How do you come back after you fail? Pick a guy follow that guy and just dive all the way in and then look at the products that he creates and Grant talks about that Because you get a lot of people out there that will say oh, I'm the guru. I did this I do that It's like great show me what you've actually created What have you produced? You know you get somebody in fashion who's like, oh, I'm an expert in fashion. That's awesome What what where's your portfolio? What have you produced? What do you have? What's the following? What do you sell or you get somebody in? Automotive same thing. It's what are you producing and that will give you a pretty good indicator of who the real legitimate person is because anybody can post content and look good Yeah, I mean What do they have where they sell? You know just Just to tell probably I Think I told you already Robin and also like everybody my audience knows The 10x rule is my favorite book of all time. I read it 10 times this year Probably gonna read it five six more times next year I listen to Grant every single day like there's not a single day goes by where I don't listen to grant for 10 minutes half an hour an hour two hours and on Grant Cardone TV I've had many rough patches in my life were even You know even the subject of money like you you kind of read it in books You watch movies, you know, you go to seminars, but it's always like this Like this thing you're trying to get to this distant thing that you're trying to go to and when I listen to Grant on On on hit on our daily hustler hustlers And just in general but daily hustlers especially You kind of it's like when you know when you sit with the guy who's that rich that successful and that easy with money He just talks about money like it's nothing And it's also important everything and then you get infected with that and You begin even it doesn't matter where you are financially you start thinking like him and I've never had that happen in any book or Or anybody I listen to it's always been like, you know, you need to get there It's about getting there and Grant talks and you already feel like you're thinking Like a rich person Right, you feel like money is abundant just by listening to him And I never got that like not not that fully anybody ever Yeah Yeah, I mean for me I Had the same experience and when I started to switch and I started to look at money It's just nothing more than really paper because that's all it is Money to me is more symbolic of the amount of attention that you can get Money to me is about the amount of confidence you can deliver about a product money to me is about knowing that I can help somebody you'll get money for that and You as an individual as a spiritual person Are so much bigger Than that piece of paper And I struggled with that because I spent I went through a really rough time. I was homeless I lost everything. It was bad. It wasn't very good. And I've been on the upswing ever since I found grant But when I started to look at money as a thing Equated to who I am as an individual is where I would get into trouble When I started to look at money is just this thing that I used to grow and expand that's where I started to shift Yeah, it's like So much My name is Robert Cislow and I have X amount of dollars. That's who I am. It's no my name is Robert Cislow I'm big I do all this stuff. I create I outflow I reach people I communicate to people when I help people This is what I want to do money is the byproduct of that money is not the primary focus It's just the byproduct that exists over here. Oh, yeah.  I like that a lot Yeah, yeah, so so you don't look at your shadow and you're like, you know Get bigger or get bigger Just get bigger as a person and that will happen automatically Yeah, yeah, I know I noticed that when you get better as a person even even if it's not even related to money Just maybe work on your fitness. Maybe, you know become a more productive person. We're a happy person You know, even if it's not immediate it always follows to some extent And I send the money Cool, Robert. So, um One last thing is for my followers I checked out your youtube channel And I saw that you upload content pretty much daily, right? Pretty much. I try to do it. I try to do it daily. Yeah, sometimes I miss it, but I try to do it daily. Yeah Yeah, so, um I believe it's it's a really really good kind of uh How do you call when there's like the opposite side of something like a Complementary To to my channel because like I told you before the interview Uh, you discuss a lot. I noticed about you know Selling in your videos and branding in your videos and you know kind of the how-tos What to actually do and you you're not like these people that talk about you actually demonstrate in the video You're like, yeah, do this do that. I it sounds like this Uh, which means you're doing it right now. You're not teaching something you did in the past No, a lot of those videos are I'm doing it on as I go. I'm like editing and creating and you're watching it happen Yeah, so so I I guess I I'm going to be sort of the catalyst for Uh people to come to you because every day or two I get somebody who's like, I'm going to start making videos because of you I talk so every day I talk about this attention videos attention videos So I believe they should go to your channel If they want to know the actual how-tos like, you know, I focus on you know How to not miss days when you want to do it how to make as many videos as possible, but I never talked about what to do Yeah Yeah, if they want if they want to know how to do it, they can come watch me. That's good. That's good. I like it Yeah, awesome. So I'm going to link you any final uh words um suggestions Well, what would be what what's something that your audience needs right now? What do they what do you hear frequently that I could talk on real quick? Oh, I mean my audience is like is like a bunch of uh of uh Coke addicts only if it's success addicts, but they're waiting for their fix They're like come on because they they need that thing that's going to motivate them Not to make a small change but everybody and and you probably know that about people in general but like everybody's They're they're not waiting, you know to learn how to start working out or to start, you know doing something small They're at the end like the the threshold the end of the threshold of like exploding into massive action Uh with what we talked about videos attention articles Uh gym meditation like I pump them full of it every day What's your opinion? About about this when should they start is it okay that they're waiting? Should they keep waiting for the perfect moment? Should they keep waiting to make their first video?  It's a fear All right, so so grant says this and I live by this, you know the motivational mess Yeah, here we go. It's gonna smack smack up pretty hard if you're waiting For that perfect video. It means you're actually really lazy Because a perfectionist and you could quote grant and say I'm take this is 100 from grant and I adopted it The perfectionist is lazy They're lazy. I mean think about it. I'm waiting for the moment. I'm waiting for that one thing to happen And when it's perfect, it's gonna happen.  Well, you are you're responsible for the threshold You're responsible for the fact that you haven't exploded yet because you decided that you needed to wait for a Perfect moment. I don't know when you put that date tomorrow three weeks from now four years from now When you finally say Okay, I think it's time to explode now. No Perfection is the lazy is the lazy way When I first started doing my streams I didn't I didn't know what I was doing. It was terrible. I actually think I still have my first stream It was dumb. I was like, uh, I don't even know if I was saying anything But I'd rather get it out And get a video out and get an article out or get something else so that people actually just start to hear money so the more Frequent you can get with the content, which is what you talk about the better it is for you So this waiting thing.  So so just undecide to wait and just I would I would I would watch this interview And I would go create something right now right like I was working on myself and then I'm like you we had the interview today and then I'm gonna do two more videos after this Write an article eat and then that'll be my sunday night Yeah, awesome. Awesome. And and I mean committing Like I find out that committing to a schedule not a schedule, but like a routine of every day doing videos um, so I committed to five videos a day and and I because I knew I have problems with integrity with the you know that idea of you know, oh, I'm not at my best right now I'm I'm angry right now. I'm depressed right now. And when you make so many videos every day It's like you have no choice.  You're angry and make a video. You're tired.  Like it's amazing Yeah, and you get comfortable now.  Damn it.  All right, great. Let's talk about this We're going to talk about it. I'm happy to do you What I what I realized when I started making these videos is that Most of your audience is you know, just it's uh, the biggest common denominator It's they're angry. They may be negative. They may be pissed. Uh, maybe they don't have anything to talk about So actually when you start a video from that place They actually relate even better because if you just wait for the higher consciousness thing where you're like feel all perfect It maybe yeah, it lifts them up somewhat But they're not necessarily relating with it because you're coming from their place And when when you make when I make a video when I'm depressed people are like I'm depressed so I can make a video as well because exactly That's the majority of what I mean, but Grant talks about all the time. It's a broken planet. Everybody's broken You know, so so you've got to think about, you know, what does the audience really like? I mean, they spend most of their time watching cats and watching the tv show The Walking Dead I mean, what are we really talking about here? Like like what where are you at? Mentally to watch the show The Walking Dead, you know So you got to think about that. So you're exactly right.  We've done a 40 minute video. I usually do I'm like, I'll just do seven to eight minutes. Like you could spare seven minutes 30 seconds 10 seconds Yeah, yeah, yeah 30 seconds people love because they're short three minutes people love because they're you know Really digestible and 10 minutes 20 minutes an hour people love because they're long and they're valuable Like I've had people tell me I love your short videos. Keep making more of those I've had people say I love, you know bite sized where I can just either, you know, five minutes here five minutes there And I've actually had students clients of mine tell me I got to your video list and first thing I look for is the longest videos because I know these are going to have the most content So I realized it's also it's important to have A super long video You know a medium-sized video and a short video to have And an angry video and a happy video and it's just a video and a good video and a bad video So true dude, it's so true You want to be married to your audience like like this is me.  No, he doesn't he doesn't be authentic Happy dad whatever that is so awesome, dude, so Where do you think you're going to be in the next Few years in terms of your development Oh, I'll be a multimillionaire I will have a high-rise condo with my girlfriend right now and I'd like to have I'd like to have the largest business entrepreneurial network on which i'm helping everybody brandy or their business And invest it in real estate and just financially in a great spot and helping as many people as I can Awesome. Well, well, you're you're following a guy who did most of these things. So So you have a pretty good, uh, you know, I I bet on your odds Yeah, it's like, how do I do real estate grad knows how do I do? Exactly awesome. Yeah, most people they need to buy his products, you know, but you can just look Hey grand, how do I do this? Yeah. Yeah. Yeah, no, I actually I very rarely ask him for advice Actually, I think I've I've never asked him for advice. I think one time I asked him What do I do? We were driving in his roles when he had the roles and we were doing a morning video shoot. We were talking about sales And I think I said to him I'm not really I was like, man, I'm not 100 on what to say.  Like the advice is there. The answer is going to be there You know, so yeah, he's kind of a living example Yes, exactly. He I also like how he keeps everything simple. So Very simple Everything is always practical. Like there's never fluff never Yeah, that's the best thing I liked about grand, you know in his books and his you know programs and when he talks He's like like step one step two step three About everything like yes Awesome, dude Cool. So, uh, thanks so much for uh, you know being here sharing your time. Uh, one day, I hope uh We could do this kind of panel with Grant as well Of course, uh, but I'll I'll be in Miami. So we'll do it in person Let's do it in person man. Let's make it real Awesome, dude. And anybody who wants to maybe Work with Grant work for Grant Any any recommendation just fly to Miami and I want to yeah, I mean if you want to work with grant you could send a 60 second video to careers at grant cardone.com 60 seconds Explain why and then you can uh, they'll prompt the sales guys to reach out to you Yeah, even even if you're the janitor you have to know how to sell pretty much That's that's basically the biggest lesson I've learned no matter what point you are in your life. You have to sell Awesome, awesome, dude. So thanks so much again And I'll put all the links in the description. So anybody who's uh interested and I expect everybody to be interested at this point Yeah, man being interested Come on Yeah, at least if you're not if you if you're still here, you haven't made the video you should have made probably So please click the links and learn more Exactly, exactly. So excellent. Thank you