Everybody forced here being 2023 Bowman baseball jumbo eight bucks case number 131 pick your team style Got Alexandros with the Yankees Bradley S twins Brandon L. Cardinals Brian H. Marlins Charles a has the Astros and the Padres Charlie C. Nationals Christopher B. Blue Jays Daniel H. White Sox Gabriel C. Orioles Jack S. Guardians James J Rays and Mets Jason G. Angels Jeffrey H With the Red Sox mariners and Phillies John C. Rockies Cody G with the Pirates Marciano Tigers Michael W. Reds Michael P with the Royals Miles H. Braves and Dodgers and Cubs. Thanks. Thank you Miles for closing us out there Scott F with the Rangers Thorpe with the Brewers Timothy F. Giants will Emma Diamondbacks and Zach D with the A's. Good luck everybody Let's go ahead and get started now Only the jumbo the jumbo this thing's about to get yeeted. It's about to get you know Is that the past? Yeah, it's Yeah The table Get that table. I don't know about literally Victor. Look at Donnie and me Yeah, we're here and the entire late sports cards team actually Is getting the I don't even know what tense that is. I'm not I don't know. I'm not good. I'm not good with it All right, so the regular base is split even the paper base does not ship you'll get all your inserts And he hits any numbered cards of course yeeton it might be yeet yote I think yeeton would be correct. Yeeted yeah Purple Rayway first moment is Alejandro Osuna the 250 Dodgers. I'm already messing up stacks Whatever base you're talking about just keeping like a separate stack the base face There's an Adley Ratchman on the spotlight Robert Perez Lunar glow Daniel Dylan O'Rei not Daniel Dylan O'Rei Go on to the Brewers So what do you think about the Reds? They're good that in the eight game win streak Donnie with the hot take they're good Guardians on hells you now first woman refractor auto it's a 499. You go Guardians Mervis What if it was a is it the front doorbell was What if it's FedEx, what if you a federal holiday USPS no no I Teen Gonzales Corbina Carol Jackson holiday Corbyn Carol Jackson holiday. Yeah Speckle first moment a 299 Union Garcia for the Dodgers Dang it. Ellie McLean steer. They got the rookies man. Yeah, young pitchers like the Dolo and Green Juan Carella first woman base auto going to the Yankees Reds or is he Phillies? I think Yeah, that is that is definitely a Donnie hot take Michael Harris rookie spotlight for the Braves any other cruise prospects It's not truly evil Well, not fully It's like everybody the US Open is good at golf People that didn't make the cut that's not true She may as well be as good as me right Sights on September awkward with 125 Phillies Andrew painter. See you Bryson. I didn't get an acknowledgement. That's cool He favored 175 Dvex Jordan Lawler.  Goodbye girl. Goodbye forever You guys say when the Conker Capnations League, they did see that right? He heard about it. They did it Donnie That's a napalm. Well, we win Conker Capnations League What is that? It's hard to explain I don't have a quick explanation. Oh well And another one Karela going to the Yankees true blue first woman out of this time to 150 nice parallel Let's see some let's see some big hits going forward here Let's do it. So International soccer separated into like Europe South America North America whatever made right Conker cap is You can look it up. It's short for basically like North America North America soccer basically it's like so it's like the It's like it's like central something I don't know good it includes Central America to and like the Caribbean. I believe that South America is like separate from Stop Jeremiah Okay, I don't know the picture. I was thinking of I know he's like you got called up the phone Ruchman sit on Raffaella. He had a good first game And then the Nations League is literally just that it's Like a tournament they play. Yes. Yes tournament. It's international. It's not like clubs They're illegal did the work that Donna doesn't want to do even though Donnie's right in front of the computer Is my Google it I just Google it Actually Donnie didn't want to bang it.  I hear you. Oh, it's just ask I think it's actually always been that I believe so and they were just like rerouted Blue jays young hella ponte on the base first bowman auto Ask Jeeves it when I was in middle school teachers like yeah, you can use Google or like yeah, we're like ask Jeeves We're all like, what are you talking about? Future is now old Lady was not it was not a man What's up? See are we gonna bring back the was ah We're gonna bring that back over Confederation of North Central America and Caribbean Association football. It is a lot. It is a lot and then there's a South America is con me ball That's the abbreviation the Paula Blue shimmer Marcello Meyer 7 of 150 nice card Red Sox boo Steve boo about to give Steve a yellow card Yeah, Steve go Donnie has no jurisdiction here. I don't Do you hear about that the submarine we're missing Like a tourist thing where they go see the Titanic. Nope. I sure did in Victor. You got some race 80s twins I'm here missing they go No, Dean you should go. I hear it's awesome. Just go down there and get lost in your thoughts, you know Among other things The first place Arizona Diamondbacks the second place San Francisco Giants The Dodgers and the fighters what are they doing? Got a downtown Ben Brown first woman true blue out of the 150 cubs last spot mojo there like one way trips That's his name Josh young on the uh something there's the right spotlight said something. Sorry. That was very lazy Cam Collier on the something There's another something it's like for first day breaking and the thing and the other thing This is bad influence for me to a person. It's like I don't want something wow Donnie's learning from the worst right now You got Oswald, Paraza. Oh, yes disconnection. That's actually the worst. No first woman light blue paper to 499 Matt Mervis Kobe's it's better than the time. I sat down broken your broken solid just in Crawford and purple chrome Brian Acuna to 250 one of the twins Michael Royo Blake Lubey a Lubey's legends on instagram Hope everybody had a good father's day and just having a relaxing juneteenth Ronnie Simon first moment refractor on at a 499 going to the rays You and your common arrow Chevy common arrow First place brewers the second place reds the third place pirates just how they drew it up The last place Cardinals Nananananana Calling Sean a little bit Kind of scary Sean here Are you Sean? Hey Donnie guess what? Your trash Oh my goodness Sean He started eating just like for pirates been not that great recently Fallen grissom Purple pattern paper is parada to 199 going to the Mets The Collier the Davis get called up for the pirates or for the I forget what You guys know check it out with dr. Steve brule I'll just show Donnie some Steve rule clips. We're gonna want to see him First bowman base auto myrochendron martinis going to the Dodgers up here there we go Oh, no Dean Oh, not bob huggins. Oh jeez. We don't have to bring up him. I was gonna say I don't get that one But I guess we're not gonna talk about it Bob Higgins So there was more than I'm only gonna say what recently happened. There was more than one reason. He was fired, but He was driving under the influence He's been the head coach at West Virginia men's basketball for like Almost 20 years a little under 20 years a refractor to 499 bryne cuny twins. So a very long time Uh driver under the influence. He resigned but there was some other stuff that he said That I'm sure is one of the uh, the reasons got you that he was basically forced, you know, whatever, right? Frilly and connoisseur on a red sox on the first bowman refractor auto to 499 Red sox What's breaking with spots, uh left on a coming up soon? We've got pearl tensor jones I can drop a link to that from yeah, dean made a driving under the influence joke Oh, gotcha that. Okay. If you ask me, that's nothing a joke around about that's a yellow le daler cruise It's kind of funny Don't drink and drive but that was that's funny joke I get a dean Raves it fillies This week Who's playing tonight red sox play twins that I think easy dub for the red sox Matt mclean reds bowman scouts top 100 on it to 99 I said reds Langaliers Three to go pro multi-sport random hit style One singular wit Yeah, john c riley is great Don't see riley's dr. Steve rule you know who john c riley is I've heard of his name. I don't like no Guys don't know who john c riley is I was sheltered from the world until I was 16. Okay That should probably give me reason to know but Yeah, the red sox aren't some really great team though So I mean the the twins are 500 the red sox are not much better than that. So there's that So 125 rookie blue pattern paper braves michael harris the second We is what's a depala? I just didn't know is that keep for it. I always forget his name Really great comedic actor. It also does really great actor. They're in like non comedies Has he been in non comedies? Yes Oh Haven't seen any of those quite a few probably more probably more Dramatic roles than comedic roles in his lifetime by by by a large margin. I would think what was the show on comedy central I did Was like on adult swim Check it out with steve with dr. Steve rule. Oh, is that okay? Check it out That was something i've always seen like memes too, but i've never actually watched the show new gangs of new york It's a great one purple carlos whore hey on the ray wave reds in 250 We got a michael harris spotlight braves lunar globe a caro nationals Thanks, steve. Donnie. I'll buy you a break spot tonight if you guess what I have for lunch And the first guess has to be the first guess Uncrustable All right. Well, you're not getting a free break spot. Nope. I had a salad. There you go There you go. That would be my second guess. No window because all you eat is salads in a crust I'm not gonna say that's not true, but it's not entirely true. I'll say that So I'll actually work eat at work I think crustable is the salad I guess recently. Yeah, what about talk about? Oh, you're never here on friday. Is he gonna talk about like every friday? Yes, yeah, I don't I'm not gonna I was a Kind of salad was how do I describe this it had it was interesting It had what the the restaurant called tandoori chicken, which was not Atomic rookie riley green spotlight seven to 150 tigers Dude atomic spotlight fire As gas straight fire. That's the heat There's also a good movie with sondra bullock and uh, melissa mccarthy light blue paper to 499 lasandro arrigas royals Heard of that one. It was either Dude, that one's there's there's there's some funny stuff in there big surprise bill burr and michael rapopore are like Brothers of melissa mccarthy in it. They're so good. So good The salad had like I i steve. I don't know man Had chicken. It had some lentils. It had romaine lettuce. I think it had some other greens in it had like a Like a greek yogurt like cucumber dressing. It wasn't quite tzatziki, but it was like thinner Yeah, I don't know how else to describe this pickled red onions smaller stuff There's some more stuff not stuff first woman based on oasis bias for the mets And I should work for a marketing company for like a restaurant. There's some stuff and chicken and some more stuff I'm sure their sales will increase like temple You like stuff we got stuff I'm sold i'm buying Chopped Caesar. Yeah, I uh, I like salads. It's good for like lunchtime and then now i'm really hungry Jones on the insert Anyway, don't need to get a free break spotty. Guess i'm crossable not a terrible gas to be honest Let's take nothing. What do you mean?  You would have won a free break spot. Oh, I get to choose the breaks for you So like it would be it would be your break though. I would still choose it Star Wars break at least I would probably I would probably have gotten you a star wars chrome galaxy Blue lunar crater to 150 you should have taken it more seriously Yeah, blue lunar crater to 150 first woman auto yeti el sanchez angels. I think I might do that next monday So just be prepared. Okay Yeti el sanchez angels sub wahoos I'll just call that a foul not an actual yellow card yet It's a warning first foul on donnie No, donnie doesn't like things like that donnie likes very simple very true burger with like just cheese things like that Spotlight at the wretchman orials, maybe a nice piece of lettuce on it That's a salad. Yeah, if you should you should chrome the one out of nine Marcelo Meyer red sox Like A salad it is stuff. That's true. It is stuff Gavin cross royals gold shimmer out of the 50 great hits Kansas City While who's kyle says hello, he's in youtube chat, but doesn't want to get twitch chat for some reason to say hello to you But he says hello too much work Future lunar crater kennedy corona the one that ain't going to the strews Kyle also doesn't play a fortnight anymore apparently Why I don't I haven't seen him on in like a week Maybe he just plays different times Scared to play a show Sometimes I have to just have to carry shaw into a win. You know, I gotta I got him a father's day to win So Dude illegal goes to twitch chat sometimes and trolls people Look at that three of five Mets red and victor simon won Congrats for the Mets We'll get this in a mag for you 75 because honestly, we don't really congrats to the to the to the metharinos rather green Figuero Gonzalez See why who's came to youtube because why who's uh is a great guy Take notes donnie Donnie never comes to chat donnie. Why'd he never get in chat? I was in yesterday for like two seconds. Yeah, exactly. Well My buddy, uh, we play call of duty. I don't know What do you guys have to say about donnie not being in chat a whole lot when he's not here?  So the one thing donnie says for the whole week in chat was jar jar speak Duncan talk I was studying the arts Donnie and big doodle this time No, I have not done it yet. I'll have to do it tonight I was supposed to set it up earlier, but You can ask donnie things things were going on around the shop today managerial stuff happened and Of course had to be manager like Yeah, there was a lot So I'll have to do that later tonight. I can defend him. I think there were 128 total. Yeah, those are 128 total spots Yeah, I'll blame kyle. I'm with that Donnie, what's your kd? Oh, I'm not great 0.6 Gary Mitchell Jordan Lawler Uh, maybe 0.4 I'll say 0.5 We don't play against like a lot of users. We do the dnz 37 pieces of flair Damon Keith Dodgers in the first woman speckle audit to 2.99. Kyle Kyle and Dylan were the were the a team yesterday Oh, yeah, ripped a bunch of personals Get a gunner Henderson spotlight Prospect Simon one I'm gonna go office space on our printer here in a little bit keeps acting up Blue pattern paper is a soryo for the tigers to 225 Tina's saying The office space is great. I need to watch that again soon purple paper rookie gunner Henderson at 250. Look at the flow. Look at the lettuce Look at the lettuce Is that what he calls his hair? Let's just call her dude the flow Lettuce the long grass the 250 gunner Henderson for the Orioles brain of walter redsox on the first woman auto brain of walter there's a Aqua lunar crater coming up here Teen Gonzalez and it is one almost the 125 for the royals Rylan bishop purple first woman auto to 250 Pirates I don't know William I don't think we have any in in queue so If personals are ordering yeah Had matt do personals after he uh finished streaming over on channel two because there were just so many in queue Oslo Montez Probably we probably wouldn't have gotten to Over half of them science. He didn't do those. Why does it sound like I have a case of the monday's illegal? I'm fine Donnie what's wrong? I Don't want to talk about All right moving on is it monday? It is monday, isn't it? Yeah, we're both here, so yeah Donnie say say something in a british accent. No I'm not falling in the middle of a crash. No, what's it meant to me? Yeah, say no in a british accent Pretty good pretty good. I'd say yeah, it's very solid. Yeah All right, lunaglow of axl sanchez going to the mariners Moving on come on case you need a big hit here.  What does that mean? Yeah, I agree with Kyle say something somebody who doesn't have a case of the monday's would say What a great day Johnny Got Miguel Vargas only insert Light blue paper first jake of barry marlins to 499. Well, yeah, this is how it goes every day I've never been on donnie making sure he's all right I mean we all have our definitions Is that what how much am I supposed to answer that question steve? I don't get it You know if I had a million dollars Go on Marvis Continue Adventure time Diamondbacks dominant kanzoni refractor first woman auto how many cards during the box 499 nine cards per pack 24 packs per pack. That's a lot.  All right, three hollow three foils in every pack Refractor wants your cone red sox the 499 Illegal is right. You did say that uh, what a great day sarcastic That's how I truly do Have a great day I don't see why it was so sarcastic about that Donnie's having a great day guys Steve clean it up. Come on About to get yellow carded jayce young tigers True blue auto to 150 Get some nice non first autos the gold shimmer cross and then the young right there What's not great about it? Oh Illegal you got a case of mondays Got a paraza rookie spotlight for the Yankees Yeah, now illegal case the money is what's so great about it. Yeah, that's exactly. Oh, man Donnie put the table on how the turntables how the turntables one karela again The third karela auto this time is a base for the Yankees first bowman You got a dog today. Higley. That's random, but okay. I'm glad you have a new owner. Oh What kind of dogs you get higley Nice friday. It's gonna be a great day Boston's hair. You're very nice.  Dude was hilarious. You're coming here. I'm saying do it like he was a Is a person That guy was hilarious Come on now. Come on now Won't ah all right. Who do we think should be in the home run derby this year? You're good He's healthy Oh, yeah, I don't think you would do it. I think you did it last year, right? Like I don't think he'll do it. I don't think vladimir gerber junior will do it again either I'll say depala why don't they like change the home run derby so it's not as injury prone to athletes It's not injury prone. It's just guys don't want to do it. Oh, yeah, but like I've heard like I could do a cop just in casa spotlight. It was a driving range. It was golf related.  They're like swings. Yeah timing and I don't know how true that is But I think it's a I think it's one of the reasons they're just like I just don't want to do it I don't they want to have I think it's partly like Partially them saying oh, yeah, this will happen if I do it where it's just like I just want the damn day off What I mean, I could see it like this is our only break in the season I'm already at I'm already somewhere like if you don't make the all-star game.   I'm sure Spencer jones He lives in florida. So he definitely plays a lot of golf. Yeah, exactly. So I'm sure he had saw the swing Nobody comes to florida if they're not trying to play golf. It's true After they retire you should do a latent skills contest.  Yeah, kicking a football all that stuff Speckle first moment auto 299 you enter Fernandez Dodgers We could have a latent skills contest Make content out of it Monetize monetize monetize monetize exactly You need to get a new hot dog world. We got to make some money Fresh hot dogs every day Donny. They've only been sitting on the roller for for six days Hey, you know what? It's there Yeah, Donny's like a scavenger pretty much We'll basketball we got tonight Donny What we're basketball we got tonight. No, I'm like none the finals are over Louise ravello atomic first moment auto red Sox out of 100 Optic and impeccable tonight of course Yeah, yeah Lava 399 Astros drew Gilbert Yeah, he thinks so illegal You think about answering my phone in middle life for anybody you crazy Like I know if my wife is still at work, I'll try to like stay up or like leave my phone on like ringer But like as soon as she gets home gets home like ah, dude And usually I'm awake like I don't know the last time that like I was off and she was working And then uh I was not like awake when she got home Once or twice in the last two years, I would say Jorge Ruiz angels and the first woman base auto Because she's disciplined she wakes up at a reasonable time does things around the house Goes to the gym and stuff that goes to work. I wake up directly and Yeah What do I do good question Dude, I'm mad at myself today Because like I got up while my alarm kicked off and everything and I was like supposed to do something I went back to bed and I woke up. I think no Give it again Drat Pretty much Then I woke up. It's like rats. I missed out on the I was supposed to go I was supposed to go to The park and fly my kite Got neon green paper rookie to 399 Michael Harris a second for the Braves Do you think I wake up when you fly it was a good day for it too today Donny? I'm sorry. It's a little breezy You probably would have had a good day flying the kite horse thinks I fly kites in my spare time Yeah, good point. Donny doesn't know how to fly kite Yeah, this would be the national don't you just throw it up and hope the wind takes it or something like that I think so I don't know. How do you fly a kite guys? I've done it when I was younger, but it was more just like My parents my parents did the work and they're like hold this and I'm like, oh, I'm flying the kite And it's that's the extent of my memory is the cost to win throw the kite up Oh, wow windy. Oh, where are the beach or like a feel? I don't know There'll be a few others too illegal Rich for a shawn is a rapper name. I think it has a ring to it I don't know if I want to take Donny's advice on the hip-hop Things does that have does that sound catchy to you? No, okay, illegal is bad at this too God cost us on the spotlight Maybe I'm the maniac Lunar glow austin charles royals followed by speckle first bowman Ylver her arrow to 299 twins Let's hit a monster here We're googling around too much We're gonna be behind ever our first break Dang it I'm just doing my job Yeah, no, it's me. It's me or do we keep talking and keep messing around and I'm doing my part Both I guess You got a hose like the Paula refractor Dodgers first bowman auto out of 499 Heck yeah Dodgers 235 before 99 There we go. There's the big hit Let's have a crazy final box of the case here. See some monsters. There's a camp collier base Drew Jones. Helly De La Cruz insert Atomic modern prospects joshobayas cardinals to 150 Gunner Henderson rookie of the year Light green paper. Elijah green to 399 nationals No, Hig No, we have to have a lot of people stay back to run breaks here Most part breaking is still taking place at the shop. You just gotta be trashed. That's it Yeah Hope Sean notices las romantes mariners on the gold atomic auto to 50 Nice great hit mariners We'll get that magged Las romantes good last box. You're not a first but Very nice low number Look for Matt Ryan's for you. I will not have time. I doubt I'll have time to even look for cards myself First woman auto for the angels Jorge Ruiz Jose de Paula all it's telling Higley sends me the big oh Here's my secret secret supply The Matt Ryan's sure there'll be so many Matt Ryan's there Matt Ryan sale So many a lot of base paper there I guess we got sapphire after this all sold out on that so baseball is totally sold out There's more baseball breaks tomorrow evening with sam Refractor our first moment is louis rodriguez the 499 cardinals Yeah, what if there are no more Matt Ryan's Higley because you bought them all that's true That's the issue. That's when Higley starts the panning Yeah, what do you do then Higley? What do you do then? Gotta start collecting Julio Jones, then I guess Gotta start collecting uh tj ducket or Vic Beasley Lunar globe one almost for the royals. How many top girly talcans cards just I don't know It would not take long this guy will at least five, okay Total print run was five of everything. Let's get the high-end falcon top girly all right autos of Yeah The uh, the numbers are a little bit thicker like a tiny bit. I think they fit good in 55 No, those are in Autos are always thicker as well All right, uh, two horror hero reases and you've got one carella brand of walter. He's used by as Myros chendrick martinis young hella ponte one carella refractors of dominant cans don't fairly in connoisseur Ronnie simon or simon on hill jenelle Speckled the 299 nana for nanda's and damon keith purple brail and bishop blue to 150 jc young blue lunar crater yada yel senchez true blue ben brown and one carella We've got atomic louis ravello insert automatic lane for the reds the 99 gold shimmer gavin crossed the 50 for the royals Uh red simon won three of five and victor metz Gold atomic and victor auto las romances the 50 for the mariners and refractor first woman autododgers 499 So say the paula All right, that'll do it. Appreciate it everybody more baseball coming up


This lecture is part of an online algebraic geometry course about schemes and we'll be covering finite and quasi-finite morphisms. So if you have a morphism of rings, say R to S, there are two finiteness properties you can put on S. The first one says that S is finitely generated as an R algebra. The second one says that S is finitely generated as an R module. So we've got these two different words here and these are quite different. First of all, if it's finitely generated as an R module, it's obviously finitely generated as an R algebra, but the converse isn't true at all. For instance, if S is equal to the ring of polynomials in X, this is finitely generated as an R algebra by the element X, but it's obviously not finitely generated as an R module because you need an infinite number of generators, one XX squared X cubed and so on. Now, for schemes, we've given an analog of being finitely generated as an R algebra. This corresponds to morphisms of finite type or locally a finite type. This one is going to correspond to finite morphisms. And you see the terminology is a bit confusing because finite type and finite morphisms are quite different. So if X to Y is a morphism of schemes, it's called finite if Y is covered by open affines VI, so this is going to be the spectrum of some ring VI so that F to minus one VI is open affine in X and say this is equal to spectrum of AI and AI is a finite VI module. So we're saying that AI is finite as a VI module. If it was finite as a VI algebra, then this morphism would be a finite type. So this is a much stronger condition. So we've said this is true if Y is covered by open affines. It's actually a local condition, so you can check this is, if it's true for some cover but by open affines VI, then this condition is actually true for all open affine sets VI. So it doesn't matter whether you take it covered by affines VI or take all open affines VI. So the first property says that if X to Y is a finite morphism, then all fibres are finite and discreet. So we'll first prove this. First of all, it's enough to prove for the case when you have the spectrum of S mapping to the spectrum of R. In other words, R maps to S. That's because Y is covered by open affine, such as the image is open affine, so you only need to check it for these open affines. So what we've got to say is suppose we have a morphism of rings F from R to S and P is prime in R and S is a finitely generated R module, then only a finite number of primes Q in S with F to the minus one Q equals P. So just to draw a picture, here we've got the spectrum of S and here we've got the spectrum of R and what we're doing is we're picking a prime P here and we're looking at the inverse image and saying that only a finite number of primes Q in the inverse image. And this is quite easy to prove. First of all, we can assume P equals zero. You just replace R by R over P and S by S over PS and you can check that this is still a finitely generated module over this ring and you're not affecting the primes whose inverse image is P very much. Secondly, so this means R is an integral domain and P is equal to naught. Second, we can take the quotient field, the field of quotients of R and again, this doesn't affect the primes who's in S whose inverse image is zero. You're just inverting all non-zero elements of R which you can assume as a subring of S. So we can assume R is a field but then S is a finite dimensional vector space over R so is an artinian ring. So remember, artinian rings are one that satisfy the descending chain condition for ideals and if R is a finite dimensional vector space then obviously it satisfies the descending chain condition. And the basic result about artinian rings is that it has only a finite number of prime ideals. Moreover, all these prime ideals are maximal and they're all open in the spectrum of R. In the spectrum of R, so the fiber of this map from spectrum of S to spectrum of R is finite and discrete. There's a bit of a problem here because this property that all fibers of finite is related to the property of quasi-finiteness and we're going to give a definition of quasi-finiteness. Well, we're going to give three definitions because unfortunately there are several in equivalent definitions of this in the literature. So growth and Dick gave a first definition in I think it was SGA1, which says that quasi-finiteness mean all the fibers are discrete of finite and discrete. He later added, he later gave a second definition of this in I think EGA2, where he added the condition that the morphism is of finite type. Hart-Shorn in his book gives a third definition, he just says the fibers are finite. And these three definitions are in equivalent so whenever anybody is talking about quasi-finiteness, you have to sort of worry about which definition you're using. In other words, you've heard, you've seen there's a problem with algebraic geometry and scheme theory, there are far too many definitions. You not only have to keep track of all the definitions, you have to keep track of everybody's version of these definitions. So the three different versions of quasi-finiteness Fortunately, in practice, most of these three definitions turn out to be equivalent to most examples. So we've shown that a finite morphism is quasi-finite. Actually it's quasi-finite according to any of these three definitions. The converse isn't true, and it's quite easy to give a counter example to this. Suppose we look at the spectrum, of KXX minus one, and this maps to the spectrum of KX. So this is just an affine line, and this is an affine line with the origin removed. Okay, this certainly has finite fibers. Obvious, the fiber is either a single point or it's empty in the case of this point here. So this is quasi-finite. But not finite because KXX minus one is not a finitely generated KX module. Finitely generated KX algebra, but not finitely generated as a module. The other slightly disturbing thing is about this example is that the morphism from KXX minus one is not a finitely generated KX module. What's interesting about this example is that the morphism from KXX to itself is finite, rather obviously it's just an isomorphism. So this is actually in some sense smaller than the finite morphism because you've taken a finite morphism and removed points from it, and it's no longer finite, which is a slightly disturbing property, but anyway. So let's just sum the relations between these various properties. So finite implies quasi-finite and this implies finite type. Here we're using growth index second definition. In growth index first definition or Hart-Schmidt's definition, this implication doesn't hold. And finite type then implies quasi-compact. And locally finite type. So finite and quasi-finite are rather strengthenings of finite type. So let's have some examples. So suppose you've got a plane curve and you project it to the x-axis. Is this finite or quasi-finite or whatever? Well, let's have a look at some examples. So if you take the curve x equals y squared and project it to the x-axis, this is a finite morphism. This is because the coordinate ring here is kx and the coordinate ring here is kxy over y squared minus x. And this is a module over kx generated by two elements. So this is generated as a module by one and y. So it's finite. So this morphism from this parabola to the x-axis is finite. On the other hand, we can take a different curve. Let's take the curve xy equals one and project it to the x-axis. And this curve is not finite because here we have kxy modulo xy minus one is essentially just the ring of polynomials and x and its inverse, which as we saw is not a finite morphism. So this is quasi-finite but not finite. So if you project a curve in the plane to the x-axis and ask whether it's finite or not, that's a little bit tricky. You have to think about what the curve is. Another example of a finite morphism is you just take the ring of integers of an algebraic number field, say zi, and map it to the spectrum of z. So here the spectrum of z has a generic point and it is primes two, three, five, seven and so on. So here's the generic point zero. And the spectrum of zi we saw, the map to spectrum of z looks a bit like a curve. So it's got a sort of ramification point and then has a point three two points above five, two plus i, two minus i and so on, point seven and so on. So you can see that this is, that the inverse image of each point of spec z is a finite discrete set. So in terms of a number theorist would say that each prime in the spectrum of z splits as the product of a finite number of primes in spec zi. But this is a geometry course. So what we do is we say this map from the spectrum zi to spec z has finite fibers. In other words, it's quasi-finite. And it's also finite because zi is a finitely generated z module, rather obviously it's generated by one and i. So if we take the spectrum of k of x, so this is rational functions and we map it to the spectrum of k of x. So this is polynomials. So it looks like the affine line. So this gets mapped to the generic point. Then this is, it is finite fibers. So it's quasi-finite according to growth and its first definition and according to Hart-Shorn. So it's quasi-finite by Hart-Shorn and growth and its one, but it's not quasi-finite by growth and its second definition. Finally, we will just show that Hart-Shorn's definition and growth and its first definition aren't the same. You have a rather silly example. Let's take the spectrum of kx.  So this is another example that's quasi-finite according to growth and its first definition but not according to growth and its second definition. And the example I meant to give quasi-finite according to Hart-Shorn Hart-Shorn's definition, but not growth and its definition is where you take the homomorphism from the spectrum from k to the localization of the polynomials at zero. So in other words, you're taking a map from the spectrum kx at zero to the spectrum of k. Now the spectrum of this has two points, a closed point and an open point and the spectrum of k just as one point. So the inverse of every point here is finite because it consists of just two points. However, it's not discrete. This is not a discrete topological space. So this is finite but not discrete. So it's quasi-finite by Hart-Shorn but not by growth and its first or growth and its second definition of quasi-finiteness. So the point of this is that if you know the fibres of homomorphism are all finite, this doesn't really tell you very much useful unless you've got some other conditions like being a finite type. In particular, it's rather weaker than asking for the morphism to be finite. In next lecture, we'll see more precisely what the relation between having finite fibres and being a finite morphism is when we discuss open and closed notions.


My name is Carl Blythe from Coral Center for OER and Language Learning and this is the room you're in, Room B, which is our lightning round room. We're having 15-minute talks, people discussing their OER. It's my pleasure to introduce our first talk of the day. The title is Grins in los Deutsch, an OER curriculum for first-year German, and our two speakers, Britt Able from McAllister College and Amy Young from Central College. So you guys take it away. Good morning, everyone. I am sharing my screen here. There we go. Good morning. My name is Britt Able and I'm here with my colleague Dr. Amy Young to talk about Grins in los Deutsch, an open educational resource for German language instruction that we've been working on for about five years now. Grins in los Deutsch was born of a Facebook grant. A colleague of ours posted her frustrations with heteronormativity and sexism in beginning German textbooks. Amy, John, Dan, as did I. We were all keenly aware of the disconnect between what our students experienced in their daily lives and what was depicted in the learning materials that we brought into our classrooms. So we decided to do something about it. Grins in los Deutsch, or GD, as we like to call it, now exists as a WordPress website with HTML5 interactive activities, and it contains a full curriculum for first-year German language. The curriculum is divided into six modules or content areas, which you see here in the box to the right. Each module includes three units of increasing linguistic complexity. The units are basically like chapters that are broken down into daily lessons. And the lessons are each based on an authentic interview, photos, text, or a combination thereof. The lessons include activities that stress all four modalities, plus grammatical or linguistic structures and cultural components. Students go through and complete all of the unit one, so all the different content areas before going on to complete the second units in each module. In this way, the students are revisiting content areas and recycling vocabulary while they build on their previous learning. The curriculum is currently being piloted at six official pilot institutions, and we know it's being used in many additional classrooms. So in the process of developing the curriculum, there were four primary goals that we had to include diverse voices to have our content be freely available to everyone with a computer and internet access, to use newer interactive tools, and to expand publicly available content for language learners and instructors. So let's have a look at some of the perspectives that we include. As you saw on the Facebook rant a few moments ago, we started with specific concerns about gender and sexuality. We took opportunities to include images of the LGBT community starting very early in the curriculum, and it's threaded throughout. We also aim to teach inclusive language so that our gender nonconforming and nonbinary students develop the skills that they need to talk about their own lives. We also want to accurately reflect the breadth of diversity represented in German speakers. Some German speakers learn German as a second or third or fourth language, and that is reflected in some of our content. We also have representations and content from people with a variety of abilities. This includes audio and video from people with disabilities, people living in collective housing with people with disabilities, and cultural information about accessibility in the German speaking world. And since German is a multifocal language, we include information about German as spoken by Germans, German as spoken by Austrians. We also include a number of words that are regional variations of either German or Austrian German. And then our second goal was open access. We felt very strongly that we wanted to have our content be open access. All of our activities, photos and videos are licensed with a Creative Commons license and are freely available to German language teachers and learners. This means that our students are not required to purchase a costly textbook, and students who cannot afford the textbook are not put at a disadvantage, something that was really well highlighted in that first presentation. And so as you may already know, Creative Commons licenses let content creators decide the circumstances under which their content may be used. As you can see at the bottom of this slide, Grendelsen Lowstoyage is licensed with a BYNCSA license, which means that our content may be used with attribution for non-commercial purposes, as long as the person using it also shares their materials under the same license. Our third goal was that we were eager to use the format of a website to seamlessly integrate audio and video directly into the lessons. And we were also excited to explore the suite of H5P HTML5 package activities available. And you can see a few examples here. These activities provide interactive ways for students to engage with the content, including standard multiple choice, true balls and fill in the blanks, but also some kind of funner and more creative activities like flip cards, drag and drop, flash cards and hotspots, which are all really useful formats for learning and practicing vocabulary, for example. H5P activities also support our goal of open access and publicly available content. Since these are, this is a free plugin, and each of the activities can be downloaded and reused and remixed. And you can see that at the bottom bar of all of these activities, there's this little reuse button that people can click on and just download the activity and mix it into their own classroom or use for their own learning. And that leads into our final goal. We wanted to build the bank of materials that are publicly available for German teachers. So we're archiving all of the content that we gathered and created in various open formats. So first, all of our edited videos, and as you can see, we have more than 135 of them right now, and that number is still growing. They're available on our Vimeo page, on the kinds in those Dutch Vimeo page, and instructors can link to or even download any of the videos for their own use in the classroom. Similarly, all of our photos and illustrations are housed in the Content DM database at McAllister College. We're still in the time consuming process of uploading batches of images, and it's time consuming because each image is tagged with keywords in both English and German for easy searching. So the big question is, how are we doing this, especially given that we are not being paid for these efforts? So this harkens back to the last question from the from the opening keynote talk. We're not being paid, and we're not earning any income from the curriculum itself. The answer is twofold to how we're getting this done. Grant funding is really important. And the fact that we received a digital advancement grant from the National Endowment of the Humanities was key. We've also received a number of smaller local grants from our institutions or communities. But I would say even more crucial to this project is collaboration. We have so many people around the world who have contributed and contributed to and dedicated many hours to this project, including many different offices on the McAllister College campus, where our NEH grant is based. We've received tremendous support from the DeWitt Wallace Library at McAllister, which actively encourages the development of open educational resources. They're doing a lot on campus to kind of encourage the development and use of OER, including small grants for instructors who are adapting OER materials. We've also received a lot of support from the Digital Liberal Arts Initiative on campus. And we were really fortunate to collaborate with a professor of drawing on campus who worked with a team of student artists to create custom illustrations for this project. That was super fun. Our board of authors and editors has worked collaboratively to shape and author the curriculum. Amy and I, as the co-pIs of this project are presenting today, but all of these people have contributed equally to Krenzenlos Deutsch. And we frequently write and present about the project together. We want to acknowledge all the other ways in which colleagues have contributed to the project. The list of acknowledgments and thank yous goes on and on. And we also want to express our gratitude for the financial support that's made this project possible. And at this point, we are looking forward to a discussion. We talked quickly and briefly thinking that it would be nice to have time for discussion. So we welcome questions. I think I will stop sharing right now so that I can see the chat more easily. Now I need to open up the chat. Let's see. I haven't seen any questions come through yet. Yeah, those illustrations. So we spent time as part of the NEH grant. I'll just explain that we spent, we brought the whole team to Vienna for a month. And we did a number of video interviews and took masses of photos that are now in that content DM site. While we were doing that, and actually over the course of three or four summers, we were able to get money from McAllister College through the collaborative faculty student research program to develop the illustrations. And I will say too that the interviews, the video interviews that we have as part of the curriculum, were developed over a series of years. So we had several phases of the project with different teams going abroad and doing interviews. The NEH grant was just for this project specifically, but of course it included our whole team of authors and editors. So it brought people in from all over the world. Amy, maybe you want to jump in and take one of these questions too? So let's see. I just pasted the link in the chat. I think I spelled everything correctly. What did we use to organize the curriculum? We used a lot of Google docs, Google sheets, types of things. At one point when we were in Vienna, we sat down with big pieces of poster paper and put post-it notes. That's how it all started and then that got transferred into a more electronic version. Let's see. Maintenance beyond the grant period. That's one of the things that we have actively looked for. So we've figured out the funding, in terms of maintaining the website, because it's not prohibitively expensive. We've also thought about leadership for the project in terms of future, because at some point, Britt and I are going to want to retire. So we have actively sought collaborators who are younger academics and younger colleagues. Maybe I could jump in and talk about tracking student progress with regards to the online activities. And I'm going to be honest about this. This is a challenge. So the H5P activities on the website allow students to do the activities and get immediate feedback. But I do not get feedback about how the students are doing. So we've worked in various different ways with this. Depending on our LMS, our learning management systems, the H5P activities work easily or work less easily. I've been fortunate that Moodle is my LMS and I can just click that little reuse button on the H5P activities, download the activity, upload it into Moodle. It automatically speaks to the grade book in Moodle. So what I typically do is assign, we work on a lesson in class. There is an expansion to each lesson for homework. I assign reviewing the lesson, doing the expansion to my students. And we have daily low stakes quizzes. I just select one or two of the activities that they were supposed to do for homework and that they consult correct. And I just plunk it into Moodle and we spend three minutes in class doing that exercise as a check. I also collect homework that has been written down and I ask students to kind of just write a little summary of what they understood and what they struggled with. Amy has had a different experience with H5P activities. So our LMS is Blackboard and Blackboard does not play as nicely with H5P and so I acquired an H5P.com account which is a paid account and that has allowed me to upload all of our activities into H5P.com and then anyone with an H5P.com account can access them. I can embed them into Blackboard as assignments and then the grade automatically goes into the grade book. It takes a couple more steps on the front end but it's really slick once it's done. There's a question here that I think is really important we tried to build page debates about captioning and what we have are transcripts that are available because of the necessity for for developing listening skills but we're happy to talk about more of that offline. Thank you.