Guilty of murder in the first degree. Have you anything to say before the court imposes sentence? Yeah, I got something to say. I just want to tell my friend, Mr. Stoll, that he's got something coming to him. And he's going to get it. The court will remind the prisoner, the district attorney, to fulfill the obligations of his office. It is therefore the sentence of this court that the defendant shall be put to death during the week beginning June 2nd, 1938, in the manner in place prescribed by law. You are remanded to the custody of the sheriff. Edward Hennessey, Associated Press. This letter will admit you to the executions required by law of Joseph Patterson, the state's prison, the night of June 4th. Check? Okay. Okay, Hennessey, move on in. Better save some of that till you come out. Well, boy, this looks like Patterson's going to get it all right. Yep, he gets it this time. Yeah, he sure killed the reprieve. Went to the governor himself. He's a tough hombre, all right, all right. Who, Patterson? No, Stoll, the district attorney. Now, you said it. All right, boys, this way, please. Is it true that they smoke when they play? Don't think about it, sonny. Patterson bumped off four himself, and how many others he's had knocked off I couldn't even guess. But when it comes time for him to pay off, look at the squawk he makes. Well, we can check off another on the old adding machine. 11 and 18 months. We're making progress, Sharpie, making progress. We'll have this town really quite the first thing you know. I wish you'd get rid of that hideous contraption. It gives me the willies. I'm not being too impertinent. Just an old Chinese custom, Sharpie. Chinese? You sound more like an Indian, if you ask me. An Indian counting scalps. It's my job to count scalps. It's still a life for a life so far as I'm concerned, and will be till they rewrite those love books over there. Thank you, Miss Sharp. Oh, thank you, sonny. You're welcome, Sharpie. The governor returned the record of the Paterson Confession. I'd like to have seen his face when they listened to it. Paterson didn't have a chance. Through with it? I'll take it home and put it with the collection. I should think you'd have enough of them now. Don't be unkind of me, this lovely morning, Sharpie. What about the mail? Oh, nothing much. Another clipping from the Tatler's column. I'm not hoping. Not a boost this time. Or maybe it is. I never can tell about those things. Read it to me. Not at all, you gossips. Not at all. The wife's boyfriend has the D.A.'s OK. Got any use of special Sharpie? No. Or Phil's a nice youngster. And you wouldn't have me keep a lady chained up in a vault at home? Or would you? No. Except that I've heard that husband should go home once in a while. And I've also heard there's more to life than crime. You certainly keep your ears at the ground. And I've also heard that tonight, if I'm not being too impertinent. Yes? Kirk and Murphy are here. Send them in. Kirk and Murphy. They've been working on the telephone thread. Yesterday's. We traced that call, Chief. Hello, Sharpie. Came from a drug store over on Fristoper Street, but there are no guesses. A lot of Patterson's boys hang out in the joint, but you can't fin it on any of them. It's a pay station. Everybody on the street uses it. Yeah, going all the time. Better forget it, Kirk. Probably cold now, anyway. I don't know.  I wouldn't worry. I figure they wanted to give me the business yesterday before I got to the governor. But it's too late now.  But prison cools them off. That'd be no prosecutors if it didn't. Burning doesn't cool off the relatives, any, Mr. Stoll. I'd keep an eye out of how are you. Patterson's got no relatives. Only a kid cousin, and he's in Mexico. Thanks, boys. Thanks. Right. You forget it. Keep moving, Sharpie. Oh, Chief. You sitting in on that quiz tonight? You bet. I wouldn't miss that. Okay.  If I'm not being too impudent? If you're not being too impudent? I'm serious about what? You're going to that quiz tonight. Of course I'm going. Yes? Oh, put her on. It's Mrs. Stoll. Hello, darling. Yes, this is a surprise. We were just talking about you, Sharpie and I. Of course it was nice. Today? Yes, this is the fifth. Yes, Lucy? I should say I do know. Of course, darling, it's your birthday. You thought I'd forgotten. I should say not. Certainly, darling, I'll be home early. We'll put on our good clothes and make a night of it. Dinner in the theater? That's right, Lucy. And, darling, there's a package on the way, but don't open it until I get there. Absolutely. I'll be home early. Absolutely. Thanks, Sharpie. Thanks. I don't know what I'd have done. Just my ear to the ground again. I tried to tell you. That gift on the way idea was an inspiration. I'd never have been forgiven. I told Traganes to send a tray down for selection. A pair of diamond clips would be nice. Small ones. I'd forgotten completely. I'm a fine husband, I am. I'll order the flowers, or kids, don't you think? Yes, that'll be fine. I'll telephone Mr. Kirk not to expect you at the quiz tonight. I suppose I'll have to miss that. Unless you plan to be in two places at once. Too bad, though. I should be in on that. Are you going home or not? Yes, oh yes, I'm going home. Don't worry, Sharpie. I'm glad of that. I don't know of anybody just now who could take your place. 10, 15, 24 left to go, Sharpie. I didn't know, Mr. Well, if you wanted the ice melted or not. Oh, no, Creole, I think it's better this way. Thank you, ma'am. Believe it. She's marvelous. She's my new maid. But you should taste her biscuits, they're wonderful. I'll taste the highball if it's all right with everybody. Two fingers, please. Don't make it too weak. Hello, Mr. Stowell. Hello. Well, hello, Jim. Hello. Jim, how are you? Hello, Jim, how are you? Just in time for a drink. Happy birthday, darling. It is now. I didn't know, Lucy. Why did you keep it a secret? All the old girls do, Elizabeth. How are you, Phil? Fine, Jim, fine. Would you like a drink, darling? I'm ashamed of myself for forgetting. Me, a cousin, too. Thanks, darling. I'll fix my own. I almost forgot myself. And I am a husband. Hello. New glasses? The sets from Phil, isn't it lovely? Birthday present? Oh, they're just replacements for the ones I break. Hmm, so you remembered. That was nice of you, Phil. It seems I saw something in the papers recently about Lucy and Phil, didn't I? Just a bit of scandal. I can't get away with the thing. I saw that. I wish it hadn't gotten in the newspapers, though.  You know, a man in my position. You're joking, aren't you? It was a triple date, Jim, and I didn't show up. The young things took pity on me. You don't think I'm serious? You don't think I suspect Lucy, do you? I didn't know what to think. You know, when you're talking to a district attorney. Well, I hope I'm not bringing my job home with me, Elizabeth. Monster, though, I'm supposed to be. Caesar's wife must be above suspicion. To Caesar's wife. Wait a minute, John. Do you know what happened to Caesar's wife? Uh-uh, something dreadful. He killed her. Deader than a darling. Oh. Well, let's just drink to Lucy. To Lucy, thank you, darling. Pierce Creola. Telephone. Who is it, Creola? Who is it? It's the gentleman who works in your office, Mr. Stowell. It's Mr. Curry. Oh. Oh, please, Jim. Oh, of course, darling, of course. What's the matter with me? Tell Mr. Cook I'm not in. And Creola, I'm into nobody from now on. Understand? Nobody. Yes, sir. I understand. You just ain't in. I don't believe it. Sometimes I wonder if Jim is my husband or just district attorney. How goes it at the university, Phil? I'm on my last postgraduate course right now. Political science. Do you know after this, I'm afraid I'm going to have to go out and go to work? You hate to give up watching football practice. Come on, Einstein. We've got to go. I'm going to make him study tonight or bust. Let's bust. A great, big, beautiful bust all over town. What do you say? Oh, you nitty. Come on. See you soon. Bye-bye. Happy birthday to you. Thank you. Good looking pair of kids. Nice, too. I wonder if they'll ever get married. Mr. Stowell. I told the gentleman you said you wasn't in, but he didn't believe me, Mr. Stowell. He says to tell you it was important and to tell you that the cousin from Mexico was in town. But he didn't say what cousin, Mr. Stowell? That's all right, Creola. Thank you. You're welcome. What does that mean, Jim, the cousin from Mexico? Nothing, nothing at all. Kirk shouldn't bother me here with details. Well, we'd better go along then. We'll have to hurry if we're going to dress. There's no place to hurry to when I'm with you. Oh, darling. These clips are so lovely, Jim. Do you know what I really hoped for? Oh, it's my girl. I bet you hoped me into them. Well, don't people say that if you hope hard enough or anything, it comes true? Only foolish people, darling. Hope's a cheat. They're not a very kind one. Must you be cynical tonight? Oh, don't listen to me. Hope is fine, darling. But having is so much better. Nice, nice, husband. Oh, now you make me feel uncomfortable. I've got a confession to make. The clips weren't really my idea. They weren't? No, Sharpie thought of them. In fact, Sharpie thought of your birthday. Oh, Jim. Oh, it's the awful truth. I forgot. Well, I wouldn't let it bother me. Sometimes I wonder how you manage to remember as many things as you do. And you're the only thing in the world really worth remembering. That's nicer than any prison, Jim. Except I didn't remember. But someday I will. Someday I'll stack up all the things I've forgotten in one huge celebration for you. And it will let me a day. This day, this nice small day, it's all right. Just having you home again like this isn't enough. I haven't been anywhere. I know, but it seems you're never home anymore. Never? Well, almost never. At first I used to be able to console myself by saying, your husband's a great soldier. He must be off to his wars. But lately it's been harder and harder making it work. I don't seem to be able to console myself that way anymore. I just want you with me, especially when it's getting dark. I suppose I'm just lonesome. Or maybe I'm afraid of ghosts. Just a minute, Lucy. Just in case of ghosts. Jim, must you carry a gun even on our night out? It's nothing, darling. What the well-dressed man must wear out. That doesn't sound like you, Jim. I know you were just trying to put my mind at ease, but you didn't used to joke about things like this. It's nothing, Lucy. I promise you. But it isn't nothing. When you scored a liars this afternoon when she was joking about Phil and me, you said you didn't want to bring your job home with you. Now you are bringing it home with you. You really mean it, Lucy?  I'm sorry, Lucy. But it isn't as serious as you think. The gun has made everything sort of melodramatic. But I didn't realize that I was bringing the job home with me. Sharpie accused me of it, but I wouldn't listen. I've been wrong. I stand convicted. Pardon me, Governor, and I promise it won't happen again. But it isn't just the gun, Jim. I know, darling. It's me. It's the job. It's everything about me. Yes, Cruella? These, yes, come. Oh, kid. Oh, this is my birthday.   And I'm ashamed of myself for saying the things I did a few minutes ago. No, I'm caught again. Caught? Sharpie thought of the flowers too. Oh, dear. Well, anyway, this is my birthday. I'll try to think of something original before the evening's over now. Good evening, ma'am. Perfect, James. Perfect. Been some time, James, since we've made an evening of it. But Mrs. Stonewell with us it is, sir. Why, James, you mean? Oh, no, ma'am. I didn't mean it. Jim, you couldn't have done it better if you had planned it. It's a great break. And all for a nick in the elbow. That's luck, ma'am, and you deserve it. I'd like to have quizzed that kid before, ain't I, and a cigarette? I'll never use them. Now, Jim, it's better the way it happened. It's a closed book. And we've had enough passes. I'd like to have had those newspaper boys in here last night when they were operating. You'd look good and sick. The dark wouldn't stand for it. We'd have had a great break in the morning papers. No, afternoon papers are not to be seized at in this town, no, sir. If this were election year, we'd get snap you right at the city hall. Easy. Just like that. Thanks, Dan. Thanks, nothing. You know favors I'm not doing myself. Well, you got this town with a year served by its long, hairy ear.  Well, goodbye, Jim. I'll be in later with the papers. All right. See you later, Ed. Oh, yes, Jim. While I was walking, I did a lot of thinking. An awful lot, Jim. Bad thing of complexion, darling. I heard those reporters talking coming out of the elevator. I couldn't believe they were talking about you. Although, one of them say the inquisitor almost got it himself.  I've been thinking myself, Lucy. Quite a lot, too. But I mean about us, Jim. We've got to do something. Hardly ever seen yours bad enough, but when... I know. I've become a regular headhunter, as Sharpie says. Do Sharpie say that? All the time. He says I've become a maniac. He says everybody's a suspect of a man. Everybody's a potential criminal. He says all I live for is convictions and executions. I never had the nerve to tell you. You didn't have to tell me. I knew it. You were what you were thinking, too. Did you really? I'm really intruding. It's Mr. Kirk, do you want to talk? Yes, I'll take it. Yes, Kirk? Fine, fine. No, no, I'll tell you what to do. You handle the office yourself. That's right. No, no, it isn't that. I'm fine. Perfect. No, Mrs. Stoll and I are going away on a trip. Three or four weeks. We haven't worked it out yet. Maybe Canada, maybe California, maybe Europe. I've never had a vacation and there's no telling where we'll end up. Thanks, Kirk. Thanks. Goodbye. Do you really mean it? Absolutely. We both need a vacation, Lucy. We both need to renew our old acquaintanceship. Oh, Jim. Yeah? You know, that trip we've been saving up for our old age. Oh, the one we were going to take for a honeymoon and dinner. Or any of those trips we should have taken and never did. All right, darling? I can't believe it, Jim. I really can't. Well, you start believing right now. The middle of the midnight sun. Nerebia. Blue Mediterranean. Then old Quebec. Australia. Nerebia. Where would you like to go, Liz? Cairo looks pretty good to me. Why not two weeks of salmon fishing in Alaska? I think I'd like to go to Switzerland. Bury a loop. Switzerland. It's so clean and quiet. Egypt's frying on a girl. It's dark and mysterious. Oh, no. Egypt's got no sense of humor. I don't want anything dark. I want sunshine and snow and everything quiet. Everything white and blue when you listen. Listen to me, will you? I'll be happy if we ever get anywhere. I still have to pinch myself to make sure I'm awake. And I'm very careful not to pinch too hard. I really can't believe it. I really can't believe it. Bracelet to match the lady's birthday clips. Your clips, Sharpie. Well, they've been gnawing at my conscience. I had to think of something myself or I wouldn't have enjoyed a moment of the trip. So you're really going? I have to, Sharpie. I haven't been myself lately. I've been somebody else. You're not telling me anything. I haven't got so lately. I'm suspicious of everybody. Well, I'm suspicious of you, Sharpie. I'm even suspicious of myself. I third degree myself. I put myself on the stand. I find myself turning round quickly to see if I'm the man I think I am. What would you say to that, Sharpie? I'd say you weren't going away a moment too soon. Right, Sharpie. You're always right. So I'm going. The moment I go out of this office, I'm gone.  And you don't know where to find me. Yes, Mr. Kirk. No, Mr. Kirk. He's not in the office. I see. A murder. But I'm not... I imagine it must be sensational. Of course. I know. Yes, Mr. Kirk. If you should come in, I'll have him call you immediately. Goodbye. And don't call me Sharpie. The sins you have on your soul, Sharpie. I'd run if I were you. No, I'm running. Thanks, Sharpie. Goodbye. Thanks. I didn't think you had that much sense. If I'm not being too important... If you're not being too important... Sorry, Mr. Stowell's not in the office, and I don't know where to find him. Oh, it's the police headquarters. I'm sure it must be very important, but I have no idea where to find him. So sorry. So very sorry. Goodbye. Sorry, he's not here, Captain. Oh, the McAllen murder. That is important. But I don't know where to reach him. You see, Mr. Stowell's gone away on a vacation. I'm so sorry. So very sorry. Goodbye. It's just an idea. Well, I've got to get a hold of him. Dr. Shaw McAllen just shot his wife. Oh, indeed. Skil Kirk. Well, it's the biggest thing that's broken around here in years. You know him, Sharpie. The Pittsburgh McAllens. Millionaires. He teaches up at the university. I'm sorry, Mr. Kirk. But Mr. Stowell is away on a vacation. Well, he can't have gone very far. He was here half hour ago. I know, but he was moving mighty fast. Yes, Lieutenant. What can I do for you? I wondered if you had located Mr. Stowell yet. He's gone. Sharpie says he's gone on a vacation. Oh, that's too bad. They're bringing McAllen over here. I figured Jim would want to question him. He won't open his mouth. Well, I'll question him. What did you pick up, Fred? Oh, the same old story. He was crazy about her and found her with another man. You know, I remember something about her. Didn't his family kick him out when he married her? Without a cent. I think I'll be going now if you gentlemen don't mind. See if you can locate the chief, Dr. McAllen.  A precise, deadly shot, Dr. McAllen. Are you sure you don't remember that? Your silence has no point, Dr. McAllen. When you shot to kill, when your gun spoke, you spoke. It's too late now for silence, Dr. McAllen. You're an educated man. You know, men have been shooting fateless wives since time began. No, no, Mr. Kirk. Just a moment, if you please. Gentlemen, if you'll be kind enough, I'd like to be alone with Dr. McAllen for a moment. I can imagine the strain he's been under. Would you be kind enough to leave us alone for a moment? Okay, Chief. Thank you. I'm sorry, Dr. McAllen. We've been so inconsiderate. Sometimes my men allow their ambitions to run away with it.  I caught myself doing that once on the way. And I was one I may not never get over.  There's no use of talking, Mr. Stone. There's no use of anything now. Do you like cigarette? I don't want you to talk if you don't feel like it. I just want you to know we're not monsters here. We're just human beings like yourself. They can do what they want with me. It doesn't matter anymore.  I'm not trying to hide anything. I shot my wife. I killed her.  I suppose it all happened suddenly. Only this afternoon. Only a few hours ago. I was leaving home for class. When I realized it was raining, I went back from my raincoat. It was then I saw her. I saw her sitting in her room before the mirror. Never had she seemed so beautiful. Sitting there in the dark, with only the two small lights on her dressing table burning, powdering her neck and shoulders, smiling and humming, happy with herself. Never had she seemed so beautiful as at that moment, with the mirror light shining up on her face, and the rain beating on the window behind her. All husbands have moments like that? And at that moment, I realized how terribly I neglected her. Well, I know it sounds horrible now, but it was for her sake I neglected her. For her sake, I worked, studied. I wanted her to have good things. And we were poor. Very poor. I understand.  And as I watched her, I said to myself, I would never neglect her again. And then I... Then I tipped her across the room to the dressing table. With her humming, she didn't hear me. I leaned down quickly and kissed her. Instantly, the moment I kissed her, she shivered. Her flesh became goose-pimpy as with cold. I saw her face in the mirror looking up at me, and all its happiness was gone. But on it was a look of a revolution. I was speechless, stunned. See, I see. The Japanese have an expression. A woman tells the truth to her mirror. And then she recovered and looked up at me and laughed and said, you should know better than to ruin a lady's makeup. She began a part of the spot on her neck where I'd kissed her. She got to her feet and kissed me on the cheek. I've got to run along. She said, I'm playing bridge at Sonya's. I'll see you for dinner. She ran out. I stood, still speechless. I watched her go home. I see. And that was how it began. My brain was on fire. I was sure there was only one explanation. She was making herself beautiful for some man. And she was going to him. She wasn't going to Sonya's. I followed her in the rain. And what finally happened, Dr. McKellen? I killed her. I know, but there are circumstances. It's all unreal to me. All blood. I was blind, insane. I saw her in her house. I went to a window. I saw her run into a man's arms.  I didn't realize I'd drawn the guns. I didn't realize I'd fired. Until I saw her body crumble to the floor. And then I knew I'd killed her. In that instant, I knew I'd lost forever. The one thing in the world I loved. It's my fault. My stupidity. I'll have to give him a lift. Don't give him a shot or something. His sleep will do him good. Did you get it recorded? Yes, sir. Every word of it. It's right there. We've got a written transcription, too. They'll send him to the chair. Did you overhear such a fairy tale in your life? The Kiss Before the Mirror. I don't know, Chief. You know that's the way things like that sometimes start. You should be smarter, Kirk. His emotional upset fooled you. Well, that was genuine enough. But the Kiss Before the Mirror story, that's something else again. Wait till a jury hears it. With the proper commenter, with the prosecution, I mean. You want a transfer facility? No, no, no, no. I could flat. I can play the whole thing through then. I think I'll take it home and lock it up. Keep this quiet. The McCallan family will probably leap to the rescue with their millions. Now the wife is out of the way. And by tomorrow, they'll have all the legal brains and the country lineup against us. They'll repudiate the confession. Well, they'll repudiate it, all right. But if we don't mention it, don't worry about it. That is until we spring it. And I have an idea, something can be made of it at the right time. It's going to be a battle, I won't say a word. Oh, you wanted it. Oh, that's something else. I forgot this earlier. I'm sorry. Terribly sorry. But I couldn't find it up, Lucy. Yes, I imagine it'll be a sensational case. Another conviction. Oh, it isn't that. I'd be shirking my job if I went away now. Believe me. It's a kiss before the nerve. What's funny? Nothing. Nothing for your pretty ears. I was just reminded of a little story I heard today. A friend of McCallan, a famous criminal lawyer, engages family rallies to Professor Zade. So they've hired Dave Morrow. The McCallan millions begin to talk. Believe me, they'll have to talk pretty loud. Well, he's down the street. There's no understanding. He'll buy his way out. I'd like to see someone try it. This is one case I'm going through with to the limit. I can understand some bohongful of boons on a Saturday night, cracking another mug skull over a craft game, but these polite, sensitive murderers, these sofisticates like McCallan deserve no quarter. And they'll get none from me. Imagine a responsible, intelligent, educated man killing another man. Oh, I've never known a lot of men I'd like to kill. Oh, I'm serious, Dan. You wouldn't do it. I wouldn't do it.  Crimes of passion, psychologists call them. Crimes of decadence, I call them. Luxuries, indulgences. Yes? Thank you, sir. Send him in. Well, Jim, I've got to run. One thing is certain anyhow. This time, you've got the people back of you. Up to now, you've been picking on the rank and fire of those mugs and bohongts you mentioned, the masses. Now, you've bagged a highbrow, a millionaire, and it'll do you a lot of good, Jim, an awful lot of good. Hello, Eddie. Well, how do you do, sir? Come on in. I'm on the way out. Goodbye, Jim, and good luck. See you later. Goodbye. Well, he had a permit for the gun, all right. Seems he used to walk back and forth to his classes and they've been a lot of hold-ups along through there after dark and he got the gun for protection. But I don't know what a guy like that would do with a gun if someone held him up. He could use a gun, all right. Ask that late Mrs. McAllum. And then use it the other man? Vanished completely. I'm going to sign a retrace of him. He was just a lodger there. Suppose McAllum knew this man. Suppose the whole thing was framed. I don't believe McAllum could frame anything. I've had a rule all my life, Kirk. Never take any human being for granted. Just think what getting rid of his wife would mean. His family is forgiveness. Return to the security of millions. A chance to follow his studies and comfort. What does he professor of, anyway? Political science. I don't remember. See what an opportunity this man would offer? It's truly neglected. He said so himself. And why didn't he kill the man? That's what a man usually does. Kills both of them. But not a professor of political science. Hmm. Now, just telling Dan Ellison. McAllum, one of those sensitive murderers. Consider that fancy tale of his. The kiss before the mirror. It's raining out. He comes back for his raincoat. Sees his wife, kisses her. She laughs at him. Suddenly he sees red. My brain was on fire. I was sure there was only one explanation. She was making herself beautiful for some man. And she was going to him. She wasn't going to Sonia's. I followed her in the rain. And what finally happened, Dr. McAllum? I killed her. I know, but the circumstances. It's all unreal to me. All blood. I was blind, insane. I saw her into the house. I went to a window. I saw her run into a man's arms.  I didn't realize I'd drawn the gun. I didn't realize I'd fired. Until I saw a body crumble to the floor. And then I knew I'd killed her. In that instant, I knew I'd lost forever. The one thing in the world I loved. It's my fault. My stupidity. Che, what's the matter with you? Look, as if you'd seen a ghost. A ghost? I don't even have a ghost but a boogeyman, anyway. Oh no, I've just been sort of moving around. No, only now, what's the matter? Nothing, nothing, just the early summer evenings, I suppose. I'm afraid I'm a little weepy every now and then, Phil. I'm also afraid I enjoy it. The first place you shouldn't sit in the dark. And don't give me that sad business about these early summer evenings.  That's it, isn't it? That's it. Sit down, Phil. I know, it's a tough break all the way around. You know Lucy, Dr. McAllen was my prof in political science at the university. He was a great little man. I imagine he was. He was like a child, so lovable and simple. Everybody at the university knew about him, his wife, except him. I wonder how he came to find it out. Let's grab on the terrace. It's so close in here. This fresh air is better. You sure you feel all right? Oh yes, I'm all right. It was Dr. McAllen I came over to talk about, but perhaps I better let it go. You seem to have enough by then. Oh go ahead, Phil, I'm fine now. Well, Lucy, it's just that I'd like to see the poor Jen get some sort of a break. I guess there's no doubt he's shot her, but... Well, I thought if Jim knew what a terrible woman she was and what a sweet little man he is, it might help. He might be lenient anyway. And I thought if you could... If I could speak to Jim? Yes, Lucy, if you could, because I could never do it. It'd be a waste of time, Phil. Well, I thought knowing Dr. McAllen... I know, but there's nothing you can do and we can do. When Jim gets on a case like this, he's different. He's a stranger. His job becomes a mania with him. I don't know him. I don't understand him. I'm even afraid of him. I'm really sorry I mentioned this. Oh, I guess it isn't as bad as it sounds, Phil. Jim's always thoughtful and gracious with me. It's just that other side of him. I understand perfectly. That's a tough right he's in. I'm sorry I bothered you. I wish I could be of help. Well, I wish I could be of some help to you, Lucy. When Jim is off on one of those cases, you know, I mean, whenever you need some laughs, why, give me a ring, will you? Thanks, Phil. Whenever I feel like I need some laughs, I'll do that. How's Liz? Oh, fine, fine, but she's ambitious as the devil. She wants me to get a job right now.  It's terrible. She wants me to give up my boyhood. Well, I've got to go. Good night, Phil. Good night, Lucy. I didn't know you were here, Jim. How long have you been home? Just a few minutes. After a walk? No, Phil dropped over. We've been out on the terrace talking. Phil likes the dark, too. Writing poetry, I suppose. Oh, no. He's one of our young realists. He libs the sort of poetry, though. Limericks, I imagine. No, popular songs, gay ones, bright ones. How's Elizabeth? Oh, she's fine. Phil says she's ambitious as the devil. She wants him to give up his boyhood. He couldn't mean his childhood good, eh? What's the matter with you, Jim? Nothing. Why? Talking like that, you like Phil, don't you? You always have. Of course I like Phil.  I was so disappointed not to find you here. I'm afraid I'm old-fashioned. I want my woman in the house when I come home. What's got into you, Jim? I was here. Yes, I know. I guess it was just when I found you here with Phil I was... You don't mean jealous to me. No. Not jealous. Envious. I envy him. I envy anybody who has a single moment of your time.  I even envy them your shadow.  How you'd gone to a masquerade and I wasn't there. Do you know I was furious? Furious because I wasn't there in your dream. Furious with all the people who were. I didn't say anything about it, but it wasn't until I got to the office that I was myself again. Sharp is right, Jim. You are going crazy. With worship of your darling. You want another waffle, Mr. Storewell? If I ate another waffle, I'd turn into one. You eat them. Oh, I can't. I was dying. A waffle, too, won't make any difference. Oh, I'm dying for my figure. I was dying for my mind. The doctor said if I didn't eat no more starch, it would take the fat off my head and I'd improve my mind. That's the telephone. Well, she certainly can cook. That's more than most of them can do. Hell, yes, sir. Oh, I'm fine. Oh, that ain't no trouble at all. She's right here. Yes, Mr. Phil, for you, ma'am. He called for you last night, but you wasn't in. Yes, Phil. Oh, what you would get. You didn't bother me at all. Yes? Oh, yes. We'll drop over later. I'll see you then. Bye-bye. Oh, excuse me, ma'am. Miss and Phil had another quarrel. I've seen it coming for quite some time. Listen, I wonder if you'd do something for me. Oh, it's nothing, but it might be exaggerated into something. Phil is chairman of the university committee to help McGowan, isn't he? Yes, that's one of the things he and Liz quarreled about. She said it took up too much of his time. Well, you can see with rumors about, like, like this, bribery and so on. It might be just as well to keep away from Phil until after the trial. I don't understand, don't you? It seems a little silly somehow. Appearances can be awfully important. If I sound like one of those husbands, you'll have to forgive me. Goodbye, darling. Goodbye, Jim. The job was premeditated, and I'm pretty sure I can prove it in court. Aren't you going just a little bit out of your way, Jim? I'm not just talking as his attorney when I say that he was not in his right mind. I know. You're just talking as an old friend. There are many criminals, and if McGowan's one, I'm giving up the profession. Believe me, if ever a man was insane, he was. So it's insanity again, Dave. I suppose you've got your battery of psychologists and experts all lined up. And when they get through, you'll have McGowan fixed up so mad you'll be asking us to believe that was his wife who shot him. Cigarette? No. But I tell you, the man was really crazy. It's the only possible explanation. If you keep on, none of us will be responsible for anything. We'll steal, kill, anything. And if the police catch up with us, we'll just go out and hire someone as smart as you to prove as crazy. That is, if we have the money. Now, look here, Jim, I'll give up my fee in this case if you'll play ball. Change the indictment to manslaughter with a recommendation for clemency, and we'll close the case. No, Dave, you can't do it. Not in run this job as I see it. A man who murders, regardless of the circumstances, is already a criminal at heart. Oh, forget the job this time.  You ought to go over there and take a look at him. Ah, I get it now, Dave. You're just giving me the human interest. No, no, no, Jim, this is no trick. A telly McAllen is just a man like the rest of us. A man who is madly in love with his wife and blind with jealousy. Why, what happened to him might have happened to any of us. Might have happened to me or to you. Stop your kidding, Dave. See, in court, he lances if you'd pinned these ears back. Well, that looks foolish, sir. Monroe's a tough and wily gentleman. We've got a fight on our hands. Chop it. Will you send two dozen long-send roses to Mrs. Stowell right away? White ones. Any card? Any special sentiment? No, just for me. They're conscience flowers. Are you sure two dozen will be enough? Two dozen will be plenty. Here's Kirk. Monroe's going to be tough. When I'll send his psychologist and expert screaming back to Vienna when I get through with him, when will I spring that confession?  You were too busy with your humanitarian studies. Your plans for a better world. Let's ask you again to answer your better consideration for your wife. Quiet up, Jack. The question is here, Adam. The dinner's here. Jack's in sustained. Please control his sarcasm. You are a professor of political science and you know that, right? Yes.  I think so. You spent a great deal of your time with them, long hours after class and in the evenings. Yes.  Is that not right, Dr. McCallum? Yes. How long would you say, Dr. McCallum, how long was it before your wife's death that you took her out, say, to dinner, to party, to the theater? Quiet, Jack, your honor. The question is here, Adam. Objection overruled. This week's attorney may continue. How long, Dr. McCallum? A month? Two months? Three months? About three months. This, then, is the woman you loved.  This woman you left to weep her heart out in her own loneliness. This is the woman you say you loved with a passion when her madness had drove you to kill? Quiet, Jack, your honor. You've been paper, ma'am. McCallum could last with all the witness saying. Thank you, Creel. You're welcome. Cracks after two-hour grilled by district attorney Stowe. Hello. It's the telephone, ma'am. Who is it, Creel? It's for you, ma'am. Yes? Oh, yes. Oh, yes, yes. I'll be over as soon as I can. Looks like you're home so early. I've had one of those days. Yes, I know. I read it in the paper. Sort of a Roman holiday, wasn't it? You shouldn't read the papers, Lucy. They're not for your pretty eyes. Nothing, Jim. I have to go to Elizabeth's for a few minutes. I wish you didn't have to go out tonight, Lucy. I'm sorry, Jim, but I have to. I'll be back before dinner. Instantly. The moment I kissed her, she shivered. Her flesh became goose-pimpy as it cooled. I saw her face in the mirror looking up at me, and all its happiness was gone. And it was a lip of a rulsion. And, Jim, I expect her. I'm waiting for her now. No, thank you, Elizabeth. I just wanted to say something to her. So I run into a man's office. I didn't realize I'd drawn the guns. I didn't realize I'd fired. So I saw a body crumble to the floor. And then I knew, in that instant, I knew I'd lost forever the one being in the world I loved. I'm going to buy some new ones. Listen, you were looking for me. What is it, Jim? Nothing. I guess the case is about getting on my nerves. I simply wanted to tell you that I wouldn't be at home tonight. I'm staying in town. Oh, I see. It's much better if I'm near the office. Yes, I suppose it is. The office is terribly important. I can get someone to stay with me here. Yes, I'm sure you can. Since now, it's just a change of the present indictment. In the form in which it was returned, in its form and in its intention. This request is quite unusual. But I beg your honor to believe it has nonetheless been most carefully considered. The jury will please retire. What's the matter with Stahl today? Can't figure it out unless he's got a new wife. He looks as if he's ill. I do hope nothing's happened to him. This is the only day I can come. He's worried, pulled something out of his sleeve. The state has come to the belief that the indictment of murder brought against the defendant in this case was not fairly unjustly conceived. The attorney for the state has come to the belief that he acted without premeditation. He pleased the court. The state recommends that this indictment of murder be amended to a charge of manslaughter. This is a serious recommendation. May the court ask what consideration led the attorney for the state so to change his conviction? An unusual consideration. Since the adjournment of court yesterday, he has had experience with a case that, to a great extent, parallels this. In fact, he's extraordinarily similar to it. And his findings in that case have urged him to reconsider this. He realizes, especially in view of rumors that have been afoot, the grave charges he leaves himself open to in making this recommendation. But he implores the court to believe that there are unimaginable moments when a man, a poor, weak man, jealous, blind, frantic, may kill the one he loves more than anyone, more than anything on earth, may kill her by some strange, tragic perversity, and in killing her condemn himself to a life of sorrow and regret. And that, not death is his punishment.  I see. I see. Please have the jury returned. The MacAllen murder trial was startled into an uproar today by District Attorney Stowell. In a scene of unprecedented excitement, the MacAllen trial came to an abrupt and dramatic close today. District Attorney Stowell asked the court that the first-degree murder charge be withdrawn. Well, that looks as if you're finally getting away on that trip, Mrs. Stowell. Something like that, Jax. You let him go? Yes, something like that, because you just come on in and miss him, Mr. Stowell. Put the next wife's life here, surprise the spectators and the court by asking if the first-degree murder charge be dismissed. The jury, following Judge Forbes' instructions, immediately returned to verdict of manslaughter with a recommendation for clemency. The penalty calls for from 10 to 20 years. District Attorney Stowell has blankly refused all further destruction of the case. We will now continue with our regular program. I don't show they was going to electrify him. Thank you, Priola. I learned a lot just sitting here on my table improving my mind. Oh, drinks outside. I know it's too late for regrets, Lucy. I've been mad. Mad. There's no other word for it. No other explanation of my selfishness and stupidity. You've always been generous, Lucy. And before you go, I'm going to ask you one last great kindness. Won't you let me start all over again? Not here in this house, not as your husband, not even as an old friend, but just as if we'd only met strangers meeting for the first time like that first snowy day in New Haven. And let me try to win you. I don't know, Jim. When you walked out last night, it seemed that your job, the prosecutor, had won. Believe me, Lucy, I didn't know. I didn't realize what had happened between us until yesterday when I saw you sitting before the mirror. When you kissed me? Yes, when I came home. I hated you, then. I just read your cross-examination of MacAllen and how he'd collapsed on the witness stand. You seemed to be more of an executioner than an attorney. I know. I understand, Lucy. And afterwards, when you left the room, I realized the truth for the first time. Hello, folks. I want you all to meet the young ladies' husbands. We were married before breakfast. I'm so happy. I don't know what I'm crying for. Come here, Brian. Kiss Mr. Stole after all. It was his wife who did it. That's right, Jim. He was really going to run out. Don't I know. When I was over there last night, he had his bags all packed. My bag, give me. All that happens in the world, Elizabeth. Thanks, Jim. I don't have to wish you happiness, Phil. You haven't. Thank you, Jim. I hate to admit it in front of two women, but I think you're right. Thank you, sir. Well, Jim, isn't there a bottle of wine on ice? Not now, Jim. Save it till we get back. Come on, Vic. Then we better run. Don't deny a griffon. Don't deny a griffon? Phil insists. He wants to be different. We're going to drive up in the river and I tied the tin can and ribbons out all by myself. And he's made one of those just married signs, too. Didn't I read somewhere about the bridge over the falls being done? Well, we can still send postcards. That was a marvelous thing you did today.  Hardly. I just came to my senses. That's all, Phil. Come on, Liz. We've got to be moving. Well, goodbye, Phil. Goodbye, Jim. Goodbye, Lucy. Goodbye. Goodbye. Good luck. Don't call me, Mama. I don't like it. You better get used to it. Hello. It's the telephone, Mr. Stowell. Who is it, Cruella? It's that Mr. Allison from the office. He said it was Moe's urgent. No, Dan. Well, I've had enough of the job. Enough for a while, anyway. That's right. No, I won't do it. No, I'm not resigning, Dan. The job's all right. The trouble is with me. I've just got a wiser myself. But, Jim, the newest-favorite boys are packed outside and there's some pretty nasty talk going on. Yes, bribery. They make out in millions. You know what I mean. Let them talk. Let them investigate. Let them do what they like. I'll take care of them all when I get back. Let me talk to, uh, Sharley. Yes, Mr. Stowell. With the greatest of pleasure. That's my little good deed for the day. Never mind that, James. And please bring the other boys back. I won't be going for a few days. Yes, ma'am. At first, I couldn't believe my ears.  About us? About me. About my great reprimation. It happened last night. Tell me. I'll tell you on the book for Europe, darling.


Hey, Psych2Goers! Welcome back to our channel. Your ongoing support is what helps us make psychology and mental health more accessible to everyone, and we want to thank you for that. So thank you. Now, let's continue.  You tell them it was just a text, and they say, but you used a period. You're so abrupt.  You write these things off as simple misunderstandings because you're not able to hear someone's tone or see their facial expressions while texting. But, what if the way you text does reflect your personality? If you text often, you most likely have a texting style. So, here are five texting styles that can tell you a lot about your personality. You might also have a blend of different ones that mean different things. 1. Emoji Texts Do you always use emojis when you're texting? You're most likely someone who is open to showing your emotions and is truthful. You want others to know how you're feeling when you're using a message. There's no ambiguity here. To make sure, the other person doesn't get the wrong idea about your messages. You make sure to express the tone of messages with an emoji every now and then. According to a study from researchers Amanda N. Gesselman, Vivian P. Ta, and Justin R. Garcia, emojis can be often used as effective signals in modern social communication. Their research suggests that emoji use may provide a reasonable proxy for expressing affection and may provide a useful aid in self-disclosure and building intimacy. As a result, using emojis with potential romantic partners may, in turn, lead to more face-to-face opportunities to assess compatibility and attraction. You are sweet, simple, and honest. If you feel happy or sad, you'll be sure to show it with a creative emoji. 2. Perfect Grammar Do you value punctuation and grammar in your writing? This love of grammar goes straight into your texts as well as your emails. This seems like a great thing, doesn't it? But in texting, people seem to think otherwise. Several studies have found that simply placing a period at the end of sentences in texts can make you come across as untrustworthy to others. A 2016 study from Binghampton University found that texts that ended with a period were rated as less sincere than those that did not. A follow-up study conducted in 2018 from the same researchers showed that one-word texts with periods were understood as more negative than responses without. With this texting style, you are most likely thoughtful and analytical. You generally don't text often and prefer to have conversations face-to-face. You are an excellent thinker and are rooted in logic more often than quick impulse emotions. This all can be the reason why you pay attention to the little details and always make sure to end your sentences with a period. 3. You Quickly Send Multiple Short Texts or Textisms Do you scatter your thoughts into several texts? Do you simply text a thought as soon as it comes to mind? If you're someone with this kind of texting personality, you're most likely an energetic person. You probably have many friends and are wildly popular, so texting is easy for you. Your messages might be quick with textisms and abbreviations. Textisms are a form of casual language used in texts identified by abbreviations, emoticons, letter or number homophones, and more. While others who don't share a similar texting personality as you might find this as illiterate or lazy texts, that is often not the case. According to a study from researchers at Utrecht University and the University of Amsterdam, only a positive effect on grammar performances and executive functions were found in texting from children. Not only may textisms improve children's abilities in written language, as has been attested in previous work, it may also enhance their grammar abilities in spoken language, as the present study has shown. This clearly refutes the suggestion that the use of textisms may lead to language deterioration. So go ahead and text away. If you're often the type to send quick short texts with plenty of textisms, it may even improve your grammar. Number four, paragraph texts. Are your texts lengthy and thoughtful? You're the type of person who understands the importance of context. You're thoughtful and generally have a lot to say. Similar to someone who texts with perfect grammar, you are detail-oriented and enjoy deep conversations. According to the relationship coach Nazanine Marzpan, if you are someone who values details, you like things that are controlled and stable. You are detail-oriented when solving problems. You're also an excellent thinker who looks at all the facts in detail before making a decision. You don't happen to be so assertive in your text messages because you aren't that assertive with your emotions. Number five, one-word responses. If you like to respond in one-word texts, like a quick good or the notorious K, then you most likely have a more reserved personality and aren't as open with your true thoughts and feelings. You may be the busy type who doesn't have a lot of time to respond. You may be the more introverted as well and enjoy spending a good amount of time alone rather than socializing. Because you are not as open with your emotions in text, you may not care how lengthy your response is. This won't phase you, though. You like to spend more time in the present, socializing face-to-face anyway. You are independent, sensitive, and often think logically about your situations. But be careful. If you're texting someone with a different text personality, they may view your short texts as negative. As research from Bingham University found that one-word texts with periods were understood as more negative than responses without. Bonus point. Did you know that if you and your friends may have a different texting style, they may not understand exactly what tone you mean to apply to your texts. A study where people were surveyed on the romantic partner found that if you have a similar texting style to your romantic interest, you'll have a more satisfactory relationship. It doesn't mean your partner needs to text you more. It simply means you need to have a similar texting personality. Leara Trubb, Ph.D., who presented the findings, said that how couples texted was more important to the satisfaction of the relationship than how frequently they texted. Did you relate to any of these texting personalities? Which texting personality are you? Are you a blend of different texting styles? It's important to note that everyone has different ways of texting in different situations. Everyone texts their colleagues in a different style from their family, and their family differently than their friends. If you ever think someone may have left you an ambiguous or rude text, it's better to just ask them in person what they meant or what they were feeling. Please like and share this video if it helped you and you think it could help someone else too. The studies and references used are listed in the description below. Don't forget to hit the subscribe button and notification bell icon for more Psych2Go videos. Thank you so much for watching, and we'll see you next time.


You may already know that salt is the common term for sodium chloride, which is an ionic compound consisting of sodium ions and chloride ions, arranged in a 3D lattice structure. You can learn more about the properties and the extraction of salt in other videos on this channel. In this particular lesson, we will concentrate on the importance of salt in our diets. Regular table salt is used worldwide as a flavor enhancer. In fact, salt and pepper are the two most common condiments anywhere in the world. Most salt for consumption is iodized. This means that iodide ions have been added. This iodized salt helps to prevent the enlargement of the thyroid glands, a medical condition known as a goiter. Besides making our food tastier, salt is also used as a preservative. It delays food from spoiling by killing bacteria and mold. To illustrate this process, let's use a piece of meat as an example. There are quite a lot of bacteria living on and inside the meat, but most are killed when it is cooked. If we didn't eat that piece of meat immediately, we could refrigerate it or we could preserve it. Refrigeration slows down the spoiling process by decreasing the optimal temperature for bacteria to survive and multiply. A common food preservation method is known as curing. Curing involves rubbing meat with a lot of salt. So if we rubbed that piece of meat with a lot of salt, a hypertonic environment is created. This means that there is a higher solute concentration outside of cells rather than inside. Osmotic pressure, therefore, is increased. This draws water out of cells, including water inside of bacteria living on and inside that piece of meat. These bacteria are killed and the meat is preserved. Most cured meats are also smoked to further dehydrate the meat and to add flavor. Food can also be preserved by pickling. Curing is done by creating a dry environment, whereas this pickling process is done in an aqueous environment. This is done by placing the food item in brine or salty water. The same idea occurs here. A hypertonic environment is created. Osmotic pressure is increased. This draws water out of bacteria cells, thereby killing them. These cured and pickled food items usually have a salty, savory taste to them. Usually, other preservative agents, such as nitrites, are added. But historically, salt is the most common preservative. Salt is also the most common food additive in processed foods. It can be found in rather high quantities in crisps, tinned food, and most fast foods. We actually need salt in our diets to maintain normal cell function, nerve cell conduction, and normal blood pressure. Too much salt in our diet, however, will lead to many health issues. It raises blood pressure, which can lead to many cardiovascular or heart diseases. The medical term for increased blood pressure is hypertension. When we consume salt, some of it is used for vital bodily processes, and the remaining is excreted through our urine. But when too much is consumed, our kidneys cannot work fast enough to remove this excess salt. This excess salt ends up in our bloodstream, causing water to be drawn out from our blood vessel cells through osmosis. What effect do you think this has on our total blood volume? Pause, think, and continue when ready. Blood volume increases, and this increases blood pressure because there simply isn't enough space for this extra volume. The blood vessel walls actually overcompensate by creating thicker and stronger cells to withstand this additional pressure. This further increases blood pressure. Untreated high blood pressure can lead to strokes, which can be caused by blood vessels in your brain bursting. Increased blood pressure also means that your heart as a muscle has to pump harder to get blood flowing through these smaller vessels. This causes the heart muscles to enlarge over time, and can lead to heart failure when the pumping mechanism doesn't work as well as it should. Decreasing overall salt consumption can prevent these health issues. On food packaging labels, salt is usually labeled as sodium. The recommended daily intake of salt is actually around 1500 megs per day for an adult, or less than a teaspoon full.


Thank you very much for the invitation to speak here. It's a great honor and a great pleasure. So everything I'm talking about today is maybe I'll start here. So it's joined work with Andrew Snowden. And the goal is the construction of integral structures on Diromco homology of varieties over number fields. So I would like to start off with an apology. This is work in progress.  I ordinarily do not like talking about things like this, but there are many people in the audience that have seen me give talks recently. So I didn't want to repeat myself. OK, so as I said, the goal is to construct integral structures in Diromco homology over number fields. But for motivation, let's sort of, and this is how we came to this problem. Let me try and recall the situation over the complex numbers first. So delta will be an open unit disk inside C. It contains 0. Delta star is the punctured disk. And I give myself the information of a family, which is smooth and projective over the punctured disk. I sort of don't specify its behavior on the boundary. So here's a picture. And the central fiber could be horrible. I don't want to think about it. But away from the central fiber, it's nice. OK, so in this situation, one has the following fundamental invariant. So it's the Diromco homology of the fibers. To each point of the punctured disk, you associate the Diromco homology of the fiber. As the point varies, you get a vector bundle over the punctured disk. And this is, in fact, a vector bundle of the flat connection coming from Gosmonin. So the question that motivates this does this bundle have a natural extension to delta? So question. All right, OK. I'll try to follow Laurent's strategy, where I only use two words. So let me give this a name. I'll call it Romani. H i Dirom of x over delta star have a canonical extension to delta. I mean, of course, it extends as a bundle. But we want the extension to be sufficiently functorial. And the answer, I mean, this is not a new question. And the answer is also not new. So the answer is yes. And in fact, there are sort of many constructions. I'm going to review a couple of them first, because the pediatric ones will be direct analogs. So the first one, it's more of an abstract construction. It doesn't use the geometry of the situation. So you start off with this local system, or bundle with connection on delta star. And you use the geometry to conclude that this associated local system is a quasi-unipotent monotromy, meaning when you sort of look at the representation of z that you get, the matrix is unipotent. And then it's a fundamental term of delaying, I guess proven here, that there is a unique extension and one can characterize it in a nice way. So it's a bundle on delta. It extends e. And of course, there are many such choices, so one has to say what one wants. So it satisfies two properties. I'll try to write them here. So the first property is that the Gauss-Mannien connection extends to a logarithmic connection. So log 0, in this case, I'm working over a one-dimensional way, so it just means I look at the divisor of 0 and I allow sort of poles of order 1 there. And then there's a second condition. So I guess I, all right, this is the answer. As soon as the family extends to not quite unipotent monotromy, or do you assume that the family extends to something to a purple thing over delta to know that there is no. Yes, I'm putting myself in the algebraic situation. That's the one I have in mind. OK, so there's one condition and the second one sort of, there's still a z-worth of choices at this point, roughly corresponding to the fundamental group. So one needs to make a distinguished choice. And the distinguished choice is that's the monotromy operator, so n, which is the residue at 0 of delta. So it simply means you look at this map and look at its fiber.  So this is a matrix. And you assume it has eigenvalues and half open interval 0, 1. Oh, yeah, sorry. No, the matrix is a matrix. And so there's a unique one with this properties, and the construction is actually functorial. So I'm going to make a few remarks about it. So this is what is called a lower canonical extension. This is quasi-unipotent, since it is quasi-unipotent monotromy, automatically you don't make the statement. The statement is still correct. But yes, so this is the lower canonical extension. And I say lower because there's the other choice, which is you still use the other interval and the other side is 0. That's called the upper extension. And these are not the same, but they're in fact dual to each other. The most interesting case geometrically n is actually no-potent, or this is the typical case. And this corresponds to this bundle E having unipotent monotromy. I mean, this is after all the logarithm of. And finally, I want to recall one last property, which is that this construction is sort of you can do it after a base change. And this is why I use the lower one as opposed to the upper one. So if you choose a finite cover G, so you just extract an nth root of the uniformizer, so I get a pullback bundle G upper star of E. Now it's a bundle on this, the copy of delta star. And I have the associated lower canonical extension there. And then I can intersect it with my bundle E downstairs. So just take the inverse image lattice. And this is E as subsets of E. So in other words, you can do a finite base change, compute the lower canonical extension there, and come back down. So this is sort of what we'll be using in the geometric setting. Sorry, in the arithmetic setting. OK, so I mean, this construction is purely abstract. It works in the land of differential equations. One sort of might ask for more geometric construction. And it does exist. And so let me sort of briefly just say what it is. So for this, you need to be involved here in ACA. So now I'm really placing myself in a situation where I can do that. So I choose some model x over delta where the reduced central fiber is simple normal crossings. So I no longer had that horrible picture I sketched. Sort of much nicer. And in this situation, you can sort of regard x to delta as a log morphism. I mean, in particular, one has an associated log-deram complex where you allow logarithmic poles along these components. And it's a theorem of steambrink in generality and cats, when the multiplicities are one, that the log-deram homology of such a model computes the lower canonical extension. So it's HI. I guess I should give. Let me go with this morphism and name F. So it's, well, I guess it doesn't matter. So you look at the relative log-deram homology with logarithmic poles along this central divisor. And you look at its log-deram homology. And there are two assertions here. One that it's a bundle. And secondly, it's sort of this extension. In particular, it has the sort of correct unipotence properties. OK. So these are the two sort of abstract constructions in our punctured unit disk, which give us natural extensions of a diram homology to the boundary. And I want to try and mimic them in the arithmetic setting. No, by virtue of the comparison, it doesn't. But it just gives us a way to compute it. So I mean, for example, you can see those eigenvalues geometrically. And this is going to be, of course, is going to be a big problem in the phiatic setting. We don't have models, and dependence is not clear, and so forth. OK. So in the arithmetic setting, let me sort of write down the result and make some remarks about it. And then we'll sort of see the actual construction. So let's say k over q is a finite extension. And x over k is a nice variety. So here, nice is actually a technical term. I learned it from Bjorn Poonen. It means proper smooth and geometrical, projected smooth and geometrically connected. I like it. It's quite short. And so the theorem is that in this situation, if you look at the, and so you fix an integer, sorry. If you look at the diram homology group of x over k, algebraic diram homology, then there is a canonical lattice in there. There exists a canonical.  It doesn't depend on the model, actually. Well, there is no model in sight. But so it's, yes. So there's a canonical lattice. It's functorial in x. And there are some other properties, but maybe I'll sort of, I'll state them under remarks. And we'll see what they are. So the first remark is that this is sort of a lie in the spirit of Jared's talk. It's kind of a white lie. If you don't actually have a canonical lattice, we have at least two. I mean, it's easy to see that if you have one canonical lattice, you can scale it by five, and you'll get another one. But that's not what I mean. There's really two genuinely different constructions. So we actually get two, well, probably different. Certainly, I don't know how to prove that they're the same. Two different such lattices. Both somehow corresponding to the two constructions I had earlier. So you can copy Doolene's abstract construction and using integral Piata-Cosh theory. And I'll give us one lattice. And then we can also copy the Steinbrink construction in some way. And I'll give us a new lattice. So there's the Galois-Theretic one. Q, Q, Q. I'll make a comment on that. So yeah, I mean, no, no, no, these two are different. You can define duals, but you get a lot more.  So they do have some properties. So if you look at sort of all of them inside the dram-comology algebra, simultaneously, then this is actually a subalgebra. So it's closed under cup products. But it is not closed under Poincare duality. I mean, this is the same thing as what happens in the geometric setting. So one shouldn't be too surprised. OK, and then where does all of this come from? The construction is essentially local. I mean, one can state it like this. But you do it locally at all primes, and then you make sure that your construction for most primes is compatible with some standard one. So what do I mean? I mean that if P is un-ramified. So P is a prime of the field K, and it's un-ramified over Q. Let's see what else. I need x to have good reduction at P. So meaning there is some model with good reduction at P. And so to assume that dim-x is less than P minus 2. And I think actually, so we need different constants for each lattices. So let me be safe and put a 3 over here, because that's the maximum one we need. So the dimension is sufficiently small compared to P. Most primes are going to satisfy these properties. Then this lattice is the lattice coming from the smooth model. So script x is the smooth model. So in other words, if you're trying to do such a construction and you are able to create such local lattices and they satisfy some property like this, then they are going to patch together. Oh yeah, sorry. Oh, oh, oh. So it really is just a local thing. But there are global questions one can ask. For example, I don't know if the determinant of this lattice is an invertible is the zero ideal in the class group. So I expect not, but it's somehow impossible to compute. For each i, each comodal g group. Yes, and all of them. I mean, yeah. It's not a good one guy, I guess. It's not a good one guy. No, directly each group. Yeah, just each group, each group, h i. Well, so by lattice, I mean a projected module. So yeah, so it makes sense. Well, I guess the determinant makes sense for any module, because the ring is smooth. No, no, that's not what I mean. It's projected. Is it clear that it's independent of the 20x? Well, it follows from the theorem that it is. But I'm saying you can define it like so. You just, a priori, you pick some good model over all of the, over like most of spec z's, eh? Bad at a few points. When you said that lattice is canonical, what do you mean? I just mean functorial. All I'm inserting is that there is a functorial lattice. And it took us a lot of work to actually see that. So in the geometric case, you have the sort of the upper one and the lower one, and they're dual. But you also know the upper one contains the lower one, and the difference is not very large. Right, so do you have a similar statement here that the upper, sort of the upper Galois theoretic one contains that it's dual, and the difference is bounded by p? Well, it's a power of p that I think depends on the hostage state weights. Oh, OK. But yeah, you have that kind of. In one of the constructions, yeah. And for, OK. Yeah. And so the wonder mark I wanted to make is that, I mean, one shouldn't really view this as a final result along this problem. I mean, there should be a better lattice. We just don't know a good way to sort of ask what we want from this lattice. We want it functoriality, and that's what we're able to get so far. But for example, you can ask if there is sort of natural torsion. We're completely ignoring torsion in this discussion, and that I don't know. So some functoriality in time. Yes, in the sort of obvious sense. Well, the question was, is there functoriality in the field? OK. But to make it clear, it's not cool. If you ramify delta star, I mean, if you ramify delta, then the pullback of the canonical extension is not so common.  There's a map. I'm not saying it's the whole thing. Yeah. So you can try to do a construction instead of models, take the projective limit of all models, and take something like omega log log. If you wait for 10 minutes, it's more or less what I'll do in 10 minutes. So I want to first talk about the Gallo-Atheriotic construction. So this is why we'll have to wait for 10 minutes for the other one. So this is the cleaner one. It comes from sort of good integral piatic harsh theory, which is my excuse for talking about this here. So this is why I left the two boards. So I'm going to have a board of notation now. It's the standard notation, but one has to say it. So p is a prime k over qp is a finite extension. I fix an algebraic closure k bar. Let's see, what else do I need? I'll need many things in a moment. This k is different. So the entire discussion is going to be local from now. And so I start off with x over k nice. Yes? And we want to construct this canonical lattice in there. And so the idea is sort of naive. And it's rather simple. You want to create a lattice in Dirac homology. That's functorial. We don't have that yet. We do have a lattice in etal homology that is functorial. And you use that. And you transport it across the piatic comparison isomorphism. Zp, what torsion, is a lattice in qp. And so we take this lattice. And so everything is gk-equivariant. Gk is the Galois group. And so you just transport this lattice along the period isomorphism. So I'm going to think of the period isomorphism as saying that d-derom of this object is equal to a Dirac homology. OK, and then, of course, I mean one has to actually go through the machinery and see that this can be done. If the field is unramified, the dimension is small, and you have a good reduction, then this is due to Fontaine messing. If you assume that all of the above, except the field is no longer unramified, then one can use Brouille's theory of S modules, and in complete generality, we use Kissen's theory of sigma modules. So I'll very briefly remind you of the main assertions from that theory. So pi, I need to fix a uniformizer. The functions depend, a priori, e of u inside, oh, sorry. One needs another ring first, which is w. So k0 is the maximum ramified subfield. w is the ring of integers. So OK, or w is totally ramified. Pi is the uniformizer, and e of u is its minimal Eisenstein polynomial. And this is still not enough, one has to make more choices. So I'm going to use the notation pi underline to denote a compatible system of p power roots of pi, sort of my chosen extension. And k infinity is going to be k adjoin all these roots, and g infinity is the Galois group of the resulting field. OK, I apologize, but so maybe one thing to remark is that this is not the same k infinity as in the previous talk. This is not the Galois extension. OK, so in this setting, Kissen defines the sort of following story. One has this ring that I'm going to call sigma, because I don't quite know how to say that. Maybe the audience can tell me what the right pronunciation for that symbol is. There's going to be another s later, so let's stick with sigma. Yeah, it is s in tech. So it's going to be the power series ring in one variable over w in this parameter u, and phi is going to be sort of u goes to u to the p, and it's semi-linear over the phi of w. OK, and so one is interested in modules over the string, and one can specialize them in sort of two ways that are going to be interesting to us. So there's w, and there's OK. And the specialization to w is u goes to 0. Specialization to OK is u goes to pi. So this is just a quotient by the ideal e of u. So with respect to this ring, Kissen defines the following categories. So mod phi of sigma is going to be pairs m and phi, where sort of m is a vector bundle over sigma. So I guess it's free, because it's local. And phi is a map from the Frobenius pullback of m to m, and it has some properties. So the property it has is that its co-kernel is killed by a power of this polynomial e of u. And similarly, one has a rational category, which I won't write down. And sort of the miracle of this theory is that this category is rich enough to detect integral semi-stable representations. And as yet, somehow, we're a much smaller ring than one might naively expect. Oh yeah, sorry, power, power for a sufficiently large n. OK, so theorem, this is Kissen's theorem. After you make all these choices and you define this ring, sorry, there's a functor. And I'm not going to state the theorem in the most generality. I'll just state it in the context in which I'm going to use it. So it's a semi-stable QP representation of GK to mod phi sigma join 1 over p. So I'm going to denote the functor as v goes to m of phi. And it satisfies the following two compatibilities. First, there is a canonical isomorphism between a specialization of this module and d dirom. So fix your v in this representation category. So there's a canonical isomorphism. It's not between just this u equals phi specialization, but you have to sort of compose it with the Frobenius. So when you go all the way down to the fraction field k, get d dirom of v. So it's some integral object that lifts d dirom of v for the purposes of my discussion. And it's not just any integral object. There's actually a nice correspondence between integral objects on both sides. So there exists a natural bijection, which goes lattices in this representation v that are stable under not the full Galois group, but G infinity. So this is a rational Cissin module, m, and you can study integral forms of it. And that's what I have here. So sigma forms of m. So integral Cissin modules are equipped with an isomorphism between the thing with p inverted and your given one. So bijection. OK, I'm sorry. I'm trying to make one point with all this notation. So the point is we can just use this to get a canonical lattice. So in our application, is there a question? So if you start off with x over k, which is nice, and you set v to be the ethylchromology of xk bar, coefficients in qp. And inside here you have this lattice t, which is the zp ethylchromology, modular torsion. Then you're in the setting where Kissen's theorem applies. So well, first need to assume v is semi-stable. So v is semi-stable. I have a lattice in there, so I get a natural sigma form of the associated Kissen module, m. So we get some m in this category, and an isomorphism with d dirom of v. Up to you, specialize to k in this manner. And by the periodic comparison, isomorphism, one knows that this is equal to hi dirom of x over k. So it's sort of obvious what to do. You just look at the image. So you define this lattice hix that we seek as the image of composite. So this is the semi-stable picture? If you change the iris and start, I mean, the uniformizer, or you change k, this is compatible or not? Yeah, I'll say that. I mean, yes, but it's a theorem. So for general x, so here I assume that the representation was semi-stable. Our priority, all we know is that it's potentially semi-stable, so there's some extension over which it's semi-stable. But then, this is why I went through this geometric construction earlier in the complex setting, where you can always sort of, the construction of the lower canonical extension is compatible with intersecting from field extension. So you just do that. Let me choose L over k finite such that we restrict it to L with semi-stable. And you define hi of x as hi of sort of XL intersected with this Dirac homology. So OK, that's the definition. The point I want to make with the definition is that it's sort of a very easy consequence of integral pi out of Cauchy theory that one can define such an object. What is not clear is that it's independent of all the choices that were made along the way. And this is, in fact, true. So I chose a uniformizer pi. I chose this polynomial e. I chose a combative system of p power roots pi underline. I chose this field extension L. And it's independent of all those choices. So we had actually proven this about two years ago in sort of restrictive conditions, meaning we needed to assume something about the hostage rate of v or the sort of difference between p and the ramification index of the field. But recently, Tonglu just proved this in general. So it's completely canonical. And moreover, under sort of good conditions, it is compatible with the sort of easy lattice, if you like. So x has good reduction. k equals k0. And the dimension of x is less than p minus 1. So you can use Fontaine messing arguments to end some sort of compatibilities between Kissen's theory, Breuys' theory, and Fontaine-Lefaye's theory to get that this is the usual lattice. OK, so that's the construction of the lattice in this sort of abstract Galois theoretic framework. It relies, I mean, obviously, sort of the main work is being done by this theorem over here. Yes? Yes, yes, there's no x needed, it's just v. Yeah, no, thanks. Yeah, so that's why I somehow wanted to think of this as an analog of DeWain's construction, where it somehow works in the world of differential equations over the disk, and it doesn't sort of think about the geometry. I mean, if you're sufficiently familiar with these aspects of integral piatic harsh theory, it's not very hard to come across this construction. At some point, I took it to my advisor at the time, DeWain, and he sort of immediately recoiled. And he insisted that there should be some sort of a geometric way of seeing such a functorial lattice that doesn't go through all this machinery. And so this is what I want to describe in the rest of the talk. So this is the geometric construction. They're both local precisely because of assertions of this sort. But if you're in a sufficiently generic situation, then it agrees with the lattice coming from a model and is independent of the choice of that model. So you can always sort of construct it as the finitely many bad places. So once again, x over k is nice. I have my integer i. And the idea, which was already pointed out maybe more than 10 minutes ago at this point, is you just want to look at semi-stable models. So if you want to copy Stienbring's construction and say, OK, pick a semi-stable model, look at the Dirac homology of that and try to prove it's independent of the choice. Of course, there's many things wrong with this. You don't have a semi-stable model. It's not going to be independent. But you can do the next best thing, which is you quantify over all models. So just look at those differential forms which become integral on every possible semi-stable scheme over your variety. And hope that this is actually large enough. So once again, I'm trying to define a lattice in this k vector space. And I want to look at those omegas which are integral on all semi-stable schemes of varieties over x. So at least this is how I understood your suggestion of doing a bigger field, bigger field. You need the bigger field. No, I thought to do it, but I'm not sure it can be done. It's a fine study of this risk-remin space. We saw, of course, there you have a lot of resolution of singularity. So I'm not sure about it. The idea was, from experience, that if you assume enough resolution, you should mimic it. But consider the log structure relative to the special 5-deck omega log relative to the log structure bound. So this should mimic the log construction for semi-stable. The problem is to prove things about it. But it's not what you do in any case. Yeah, I mean, in the arithmetic setting, another problem is the multiplicities. I mean, you can have sort of peas in the multiplicities of the central fibers in, if you assume, resolutions. But OK, so I mean, this is the idea. And I would like to formalize it on state of proposition. So let me make the following, define the following category. So ss of x, it's just going to be, I mean, this, semi-stable varieties over x. Except I want to sort of state it formally. So it's going to be diagrams like so, where x is your fixed guy, this is some morphism, and y is nice over some field extension, which is finite over k. And it has a semi-stable model, namely x. For a lot of what I'm going to say, you can actually replace semi-stable with the log smooth of Cartier type. You mean OK with it? OK with it. Oh, yeah, sorry, OK with it. Thank you. But let me just sort of stick with the more intuitive terminology. OK, so these are all the collection of pairs I want to work with. And the one sort of naive observation is that whenever you have such a datum, y, y, and x, you get a log scheme, which is this guy, y over OK. In particular, you get its log-deromcomology. And this gives you an integral structure on the algebraic-deromcomology of y. F can be any morphism. F can be any morphism, absolutely. So you can sort of, there's two games you can play. You can either put conditions on F to make it easier to show that you get a lattice, but then you have to work with to get functoriality. I'm going to just work with all morphisms of functoriality we built in. And then the hard work is to show it's actually a lattice. So I'll use different notation, Mi, because it's not equal to the lattice from the previous discussion. So this is going to be all classes here. So F upper star of omega is integral on each of these triples. I mean, this is obviously functorial. If you have a map from x to y and an object over x, you get an object over y. So this subgroup or sub-OK module of my deromcomology is clearly functorial. It's also clear that it's compact, because there is some lattice on which it's integral, so you can intersect back down and you get something nice and small. The only non-trivial content is that every, so this is large enough. In other words, whenever you have a deromcomology class, say omega, there's some multiple of that class, which is integral simultaneously on every possible semi-stable scheme that lives over your x. And so that's the proposition. Maybe I say this is one and two. It's the analog of what I had in the previous construction. So if x over k is good reduction, k is equal to k0. And here I need three dimension of x to be small. Comes out of the proof. Then this is equal to the lattice coming from a model, a modulation. So in other words, if you do this globally, then you actually do get a lattice. The age of gluing of the integrations of helicopter base extensions?  I'm not doing any homotopy theory here. I just fix my rational vector space and I just search for things that are integral in there. I don't sort of care about if they're homotopic over the double overlaps and so forth. So I mean, I don't know a nice shifter at a grade of saying this. OK, so in the remaining part of the talk, I would like to explain what goes into this. And at least from my point of view, there's a lot of technology that goes into this. So some of it is known and we had to sort of discuss, develop extensions of some known things. So I'll try to explain what they were. So the idea of the proof is very simple.  Now, we have no idea how to do this a priori. Like, you have some model and there'll be some multiple that works and then there'll be a larger model and there's some other multiple that works and there's no compatibility in this process. But there is compatibility on the side of piatic etalcomology. And so the idea is to have an integral piatic comparison isomorphism between Dirac and etal and then try to use that. So does what depend on the vanishing theorem? No, no, it's not going to depend on my vanishing theorem. It's going to depend on a slight extension of De Jong's alterations work. So you use integral piatic comparison theorems. And I said theorems in quotes because one doesn't have such isomorphisms. They're only maps. But the maps have sort of bounded kernel and co-kernel and we can try to use that information. OK, so here are the main tools. And I will sort of work in a slightly different setting. So I'm going to assume now that this x is semi-stable.  So I'm going to assume x over k is nice and has semi-stable reduction. So semi-stable model, say. Script x over OK. And d is going to be the dimension, the relative dimension. So I want to tell you first what these integral comparison theorems are. In order to do that, I can't just work with Dirac homology. One has to work with a slightly richer object. So first, I work with log crystalline homology in sort of the ramified sense. And let me sort of tell you. So I have this log scheme, x over w. x is given the log structure coming from the fact that it's a semi-stable scheme over OK. w is given the trivial log structure. And that gives me a site, the log crystalline site. And this site has a morphism down to the log crystalline site of just the base. We'll give this a name, f. And so associated to this datum, you can do homology. So in particular, you have the push forward. So rf lower star of ox over w lcris is an object. And so it's a crystal. It lives on the site. And it's sort of very instructive to think of it as a crystal, but just to understand the functoriality. But to work with it, I'm going to use a specific specialization, which is Brouh's ring. So I'm not going to need Kissen's ring anymore so I can delete this. And so I'll do the analogous thing. So once again, let me say in words what I'm trying to do. I have this crystal, and I want to access its values. To access its values, I have to tell you what it looks like on a really large PD thickening of OK over w. And that's what comes from this choice of. So s is you take w adjoin u, the polynomial ring. You join divided powers of the kernel of the map from w u to OK, which is given by setting u to pi and you periodically complete it. And so this is a Versailles PD thickening of OK over w. So in particular, it makes sense to evaluate this crystal on that thickening. And the result is what I'm going to call e chris of x. It should really be script x. So this was a sheaf on the crystalline sites. So when I evaluate it, I get an object on each ring. So I get an object of the derived category of s modules. And this object has really nice properties. So one needs some of those properties. So the first property is that it's perfect. I mean, it is very tempting to just guess that each of the individual comology groups are nice. I don't know if that is true. I certainly don't know how to prove it. One does know, just by sort of easy derived arguments, is that if you look at the full complex, then it's a perfect complex. But since I don't even know if this ring s is coherent, I can't say anything about the individual groups apriori. Secondly, by functoriality, it has some natural structures. So it has a filtration, has a phi action compatible with the induced phi action on s. And it has a connection, a logarithmic connection with respect to parameter u. Yes, yes, yes, sorry. So yeah, this object certainly depends. Yes, I mean, the structure you've upstairs is an object of the filtered derived categories. I take the push forward in the filtered sense. OK, so I mean, these are some abstract properties. And what does it actually look like? Well, to actually look like, I can only tell you what it looks like when you specialize. If you specialize from s all the way down to OK, so this is u equals pi, then in fact, you get Dirac homology. So E Chris of x, 10 set over s with OK, is the log Dirac homology of this model. So in that sense, it's reasonable. Once again, if I had to say something at the low of individual homology groups, I would be lost. So let me stick with the complexes. And similarly, you can do the other specialization, which is u goes to 0. And there you get the log crystalline homology of the central fiber. So it's the usual situation one has when one studies a Bray modules over s. You have two specializations. One of them is related to crystalline homology, and that's where the Frobenius is coming from. The other one is related to Dirac homology, and that sort of detects the filtration. OK, so what do we use about these objects? And what do we prove? So the fundamental fact that makes the complex amenable at all to calculations is the Hiotokata isomorphism. So one needs to know something about the homology groups. And so this is what I'm going to call Dwork's trick. And the assertion is that, OK, this complex would be horrible, but after you invert p, one has some control on it. So theorem. So I mean in the non-log case, Sperthelogus Hiotokato in the setting I'm in. And Baylinson gave a really nice explanation of this without somehow using explicit complexes. And it asserts the following. So as you take this complex and you invert p, then, in fact, this specialization, the 1 du equals 0 detects everything. So OK, this can be literally true. This is living over w. This is living over S1 over p, so you just extend scalars. So in other words, first of all, you can find a section back from the u equals 0 specialization. And then you can do Dwork's trick to conclude that it actually extends to an isomorphism like so. But it has the following consequences for us. Now one can actually say something about the groups. So at least this one is nice. Here, I mean nice in the non-mathematical sense. I just mean it's a free guy. And the second consequence is that if you look at the map at the integral levels from integral H i of E chris to H i d'Rom, so the u equals pi specialization, then the image is a lattice. So if I'm trying to prove something about d'Rom homology, I can always live classes to here up to a fixed error depending on this model and try to work with crystalline homology instead. I'm sort of running a little short in time, so I apologize. OK, so the main ingredient, which is sort of absolutely where everything all the control comes from as you go across models, is the integral piatic comparison theorem. So I will simply say in the interest of time that there is a natural map like so, S to A chris. A chris is a Fontaine's A chris. And the map is you send u to pi underline, coming from my choice of a compatible system. This is not Galois equivalent. It's only G infinity equivalent, but that's fine. So the theorem, so I mean I learned this formulation of the theorem from faultings. This is work, but I mean I'm not an expert. I think it follows from many of the other approaches as well. So it says that there exist maps back and forth, which relate E chris of x to piatic etal homology. So Cx goes from E chris of x, tends it over S with A chris. And on the other side, you have etal homology called that dx. So the first map is the one that comes from the comparison theorems. It's the one that's compatible with the algebra structure. The other one, the backwards one, is induced by duality. And the composition is just multiplication by t to the d, where t is the usual period of 2 pi i. So it depends on the choice of a compatible system of p power roots of 1. So Cx depends on the model? Yes, yes, yes. Sorry, I keep doing this. So swing it up. In this entire discussion with E chris, it depends on the model. I mean I wouldn't know how to define E chris without the model. No, well not because of the theorem, but other than that. I mean I don't know what the question would be if you didn't take a model. Yeah, so my question is about left answer depends on the model or not. Well not because, but no, but because only because of the theorem. Well, left answer depends on the model, right? Oh, sorry. It doesn't depend on the model. I don't quite see a direct way to say this, you use the rational comparison isomorphisms. You have Piata-Gittal-Comology, it doesn't depend on the model. You get filtered phi n modules and then that's what that one is. Yeah, sorry, thank you. Okay, so I'm out of time and I was just about to get to the things we did. So I'll sort of simply state them in a few words. So once again, to prove this boundedness, we first live from Duram-Comology to Crystalline-Comology, which is possible by Dwork-Stragg. You then move from Crystalline-Comology to Piata-Gittal-Comology, which has a bounded error thanks to Fulton's integral theorem. And then you sort of try to argue on the side of a telecomology. To actually do this argument, we need sort of two more ingredients. And these are both of geometric nature. So the first, in Fulton's theorem, the error depends on the dimension of the variety. If you're working with HI, you want the error to depend on I, not on D. You could be working with H5 of a thousand dimensional variety and you want the error to depend on the fact that it's H5. So one needs some sort of a left-shits theorem for these groups. So there is a very weak left-shits for Ecriss. When I say very, I mean, I don't assert anything for a specific hypersurface. I just assert that there is some hypersurface where the usual injectivity and surjectivity properties hold. And this really uses the perfectness and a recent result of Jensen and Seito on Bertini theorems for lock schemes. And then the second ingredient in the Nalstow is sort of Deong's alterations plus something. And so the result we need is that in the proof, we want to make some alterations in a way that they're etal at a given point. Now, one can do that, but one has to actually prove it. So some control on the etal locus, meaning if you have a variety and you're trying to prove semi-stable reduction, Deong will tell you there is some alteration which has semi-stable reduction. But what we want is actually, when you fix a point downstairs, you can choose that alteration to be etal at that point. Find that etal even, which has semi-stable reduction. And you can do this for sort of all points. And that's what we have to prove. So, okay, I guess I'll stop here because I'm out of time. Sorry. So we wanted to talk about a question. So the semi-stable category, you make trajectory because you set proper and later on you do directions. Yeah, I should have said trajectory. Thanks. Two, two. Is there any distinction with a question about the A and the E? Not this construction, no. But what I, what one can say is that, so if you have this improvement of Deong's theorem, in Balanson's paper, he uses the H topology on the generic fiber. And what this allows you to do is work with the etal topology on the generic fiber. So you only ever do blow-ups and alterations along the boundary. And this brings it a lot closer to the original. You have always been using it as a model and she's been trying to do it in topology. So what do you do? Isn't there any relation? I'm sure. You could recover by taking the organa, A and sense. I mean, this is what the other show was asking about. This is what I wanted, I'm interested about waiting on what you showed. I couldn't get it to work because of the homotopies. I mean, you're not just saying that you have your class which is integral simultaneously on all models. If you do our gamma, you're somehow saying it doesn't have to be integral on all models with some homotopy on the fiber part and a double homotopy. At least, I mean, I didn't try very hard, but I couldn't see it. It's not enough to take all alterations with the misstable model or the original model. It is enough to get a lattice. But it's not, obviously, functorial unless one has something like this. Because. It's not flowing, but no, it's the same. No, I don't know if I got the same thing. We can control the error depending on the dimension and the ramification index of the field. In fact, that's how we do it.  Painfully. You go through all of De Jong's proof and observe that at each step you can do this. I mean, Gabor told me that he knows how to do this and maybe he knows a better way. I don't know. So it's over, no, but actually, if you do it over one dimensional bed and characteristic pick as you have to introduce the separable thing. So this is a tile means after extending to. Yes. But here it's a number of field case. But it's, I think if one looks at the case over a field it's not more or less easy to see the choices in the young original paper over a perfect field case. And then the one is just choosing generally not. Yeah, okay. So I mean, this is. It's really. Yeah, I mean, that's what we did. We just go through each step of the argument and observe that you can make those choices correctly. Yes. So if I understand, so your first course of time you must be used in comparison between the tile comology and the arm comology. And the second one is rather between the arm comology and the arm comology. The second one, it seems natural that maybe it's out of reach to get the derives. So maybe that is a better complex. Yeah. I mean, one can try to define something locally by saying you look at Piata-Gatalcomology, you tenser up with a Chris and then look at the right Kalwa invariant. Oh, but you can rather use a complex like this, I mean, that's what it starts to believe in. The torsion is completely different and the pistons are the same as the arm comology. All right, no, I don't know. I mean, yeah. So you get two constructions. So one line is bigger than the other or do you have some relation between them? Do I have a relation between them? Yeah. I have totally everything I know which is that if P is sufficiently large in the, but other than that, no, I don't know.  And for the other one, I pick some semi-stable model and then intersect. So, it's containment. And they're genuinely small. So I think if you compute the case of an elliptic curve with hospital reduction, you get a difference of P. Do you need more Chris? Okay, this one's got a speaker here.