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Non characteristic finiteness theorems in crystalline cohomology
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Title  Non characteristic finiteness theorems in crystalline cohomology 
Title of Series  A conference in honor of Arthur Ogus on the occasion of his 70th birthday 
Part Number  1 
Number of Parts  12 
Author 
Berthelot, Pierre

Contributors 
Abbes, A. (Organizer)

License 
CC Attribution 3.0 Unported: You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
DOI  10.5446/20243 
Publisher  Institut des Hautes Études Scientifiques (IHÉS) 
Release Date  2015 
Language  English 
Content Metadata
Subject Area  Mathematics 
Abstract  On the crystalline site relative to Z/p^n, I will explain the construction of two triangulated subcategories of the derived category of complexes of filtered modules on the structural sheaf, linked by a local biduality theorem. For these complexes, one can prove finiteness theorems for inverse and direct images which are analogous to the "non characteristic finiteness theorems" in the theory of complex Dmodules, and one can generalize the classical finiteness and duality theorems in crystalline cohomology. 
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00:03
so many things and there are thank you very much and still thank you I'm affiliated to the organizers because it's really good for me to to speak at the sentencing system of possible we had setting for the 1st time in 74 on we're working studying comedy from the very beginning and now I'm returning to encouraging gains so think possible freed circumstance to the nevertheless is not adopted a new work by far and I have to apologize to those who have held earlier versions of this we suspected overdue gave took on the role that the conference was due increases this isn't Dokic said that no there are slides and that's popular results of fossils insistence for me to lie down completed his research which I have not changed to let the distance away from you thank the keys advice seriously OK so I want to talk about Christa encourages him might be to the end of the tied to the marginal fired mestizos examples which are physically known so the additions on interdiction women annotations based upon number and integer reworking would be to the end give it would be a perfect of characteristic being individual liberty when the fate of the victims of land and descriptions in the case
01:39
sold no never consent emerged from proper it is over OK we suspect individual and entity would cover that's because we mean fishing so fast that there is a more frequent and coverage office was 15 when there exists such a lifting the 2nd the complex of percentages in the last sentence is a buffet complex of the review and would use and felt that it satisfies Park Avenue so that is all you will find things in literature and there are some of these results in most or all of these results which can be generalized to look at Free French and generated crystals the standard scientific zeal but beyond his ours this century things about 20 minutes of "quotation mark perfection pointedly date for modern art coefficients so I want to introduce beyond category of questions relating to the UN will fall which I will have similar results from . 1 2 3 which I just quoted and I wasn't just whenever it's possible military veterans of the cooperatives Norris a whenever it's possible but they should props a platoon flat here because we do not expect to and from former reasonable within the 6 operations and work stuff and because we know that Justin CalEnergy as the fight is not working properly or not knowing things on the report from the schemes and the soul from I certainly would usually has some problems for musical about which required to work with more generous shades of difference repair does so I won't enter into that year but they would commit myself to the Crist despotism sector so what are the reasons that I can give to that I assume that X 0 is a smooth case came in as new means that the review and will excellence works the organizers to even if history inside which would be the new but inside there and I would want to do time in the categories of .period complex of for 0 modules which I call deep African Chester effect which of the following properties if you assume that it is the stable and then contacting always are respectively equivalent and untie equivalent to the category of best effect complexes of dualuse duties during of edition us as the 1 afternoon this hardened which are sometimes denied by the 0 enlargement million no there's still that is after extended by will permit duality theorem that's all during the daily we don't lifted off gossip it's felt haven't put out a similar simple equipment space as part of the careerending injuries and identify the notion of an uncharacteristic morphism between 2 small schemes with respect to the complexity of any the the on 0 and
04:41
when we make a nonfactor the consumption then can have some find it necessary light through the fireside Nestle .period continually so as I said I would be working with opinion input on Tuesday inside because I need to be able to associate the threestory onefifth of history to win a 5th of the module I had some for about similar results should be toll for shades on the Nunavut science items which would then to include OK speak would do but this is probably killed because there isn't it would answer condition to London because of the injury history inside and they have a completely clarified the soul of the fury will apply to the nose skin contact conductors usually know as we the catalog structure then you can issue assume that look scheme satisfies the leisure complex for equipment the idea of an different chief to be able to apply to didn't have the same reasons followed him was that also in the catalog such either put back in the you pull back from the new thing of of the injector us to kick and then you go to the region of Kibuye tension in a map these units so need to find no deep affections so I got to download North occasionally and utilization of those came 6 0 over and I 0 and most U.S. isn't giddiness and different ways of getting proponents their as season I'm utilizing the power between the end of the mentioning introductions and exile will be useful says all skin of British and awarded the dimensions d on the exgeneral India and sometimes you may have to be to dangerous that 9 the export important then I know my exit thing the extreme media chief of the different apparent doesn't know so soon felt that this was listening is given X yeah sure it not so
07:11
category 1 was a affronted switch unit in this by exiled former after the excellent used to increases of weeks to Woods's your eyes module forecasts which is which is equal to define it should take a thickening the press insight and it's an important international and so as the X is its most of the fires you can extend the deal and not from you 2 takes To has enough it's from to acts this map is not unique to the pullback is in fact will be fined up to 10 egoism offered his thanks to the Benedetto formula and you can know when the seagoing varying the precise insight and the defined as chief of the OIC's will arise modules
07:58
and most basic prophecies of onestop with some encouraging that is this is an agreement of categories between the category of Dixon use undergirding of the stars which is essentially a subcategory of for example Reisman however you should and so on only
08:23
2 1st he should pay attention
08:26
to the fact that 6 0 0 is not an exact from Tom even those you begin Americans and acquirers of categories which is that the inclusion of crystalline worlds away rising would use is not noted exact from died said he's because you defined 6 0 my leading backed by his new confirmed that the age of the stock which extends the supported on flat in general I also have the resources to help the yes because its agreement with if the module but the galleries understanding the getting of resources and getting for weeks you'll realize mutual funds from the government of people is not a true story so she went as a sports fans in the sense of humor annuity the did the majority of the governor of Kennedy when was with feathers and commuters sticking sixes off laughter so whatsoever from the influence which is not to win and what they are getting out of the previous proposition so we are 6 0 0 and I would shift the provincial compatibility with functions in and they would I will need by zeal the she from the minus 1 of the experts from from the minus 1 of the exit minus 1 for exhilarating which is obtained by dividing the 6 0 0 that is increasing in a complex of the module influxes of additional parties something which is pollution by menus which are flat lower its and then issued by the year the storm myself from so the 1st In
10:09
addition the whenever the going and the present site on the complex a few injuries in the dark category I can find a complex which is introduced and sickening today which I will unite that did it is because the photo which assists associates to units value and he continued its exact from so with this definition again defined Tristan complexes as being the complex's foliage the Government Accountability condition not any more feasible 2 of the gaining 20 . 2 2 is an item off in the last category this means is that there has not been defined on increasing in the complex in the mind flatly dilution of the or excessive overall S and then taking the position of the stock of the situation over the rules for the citizens of the price so those complexes that we fought for studying know that the other ,comma issues on the 5th and insight is not engine on the outlook in general system crystals and that's a good example of such a complex issue Dickerson most morphism of schemes and is almost wiser than the the the dieting major for example is presiding over progress of softball on the side of nutritional flies all over so I want to this from down sales at all and I would use various subcategories of the categories of complexes of forces overall as majority and we do not minus lower fees the full subcategories consisting of prison complexes DFT India for over lies with the complexities of finite tolerance and as usual and DQ CEO Foley's although I in the forms of getting only for compote of complexes which of course the current values on which the to and some time and we collect these indexes In the
12:15
complicated things about the disarmament accord it's an intestinal for these categories so you have which of course is the consequences of the definition of the front of ceramics 0 0 so 1st of all as I said no I didn't say but it's easy to check whether everything that happens the year ecology don't buy flat is edition the compression getting depressed complex so it's fine all the mention of Oleg 0 if only if you start and with a complex of the media which is defined on mention of the unfurled its quizzically underfunding eliminating the initial complex of the jury was classical so I want to characterize the view the essentially manager of the complexes which of 5 fold the and unequivocally went over the X my search for granted it is my immediate goal so do you think I will use
13:19
the fact that there is a lot that joined to the front door of 6 0 0 the following week authorities this by using the politics of presiding tho posted I skied post which is pleasure originated by you it the as so it you 1 buying those images for each going take president will you it's 0 0 as minus 1 of the value of federal review so again values this with all the shit DX success the axes buying when you're on the left the XMen alive basement you like application so pricetag 0 to DAX was viewed as a left the examine you and what do you get you get something which is unknown actors will rise you learned in preserving the Exuma news might previous construction but you constantly Tunstall this action on the riots so you get a social environment which otherwise action by the sheer few minus 1 over as of DX the the the you know
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way you can associated maneuvered to a new exhibit Verizon you take 1st of all the bonds of OIC's 0 over as only consul vise president also binary use the example of the eggs into the ocean and unbending project and is on the site citing to get to the phone bill which I used by a mix of so long as this case shows that is hiding so we can also dehydrate and then we by DMX selfevident disease died from Dell posited by miners in the year so than from the definition units this is the
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properties In 1st that again defined from its oil makes modularization depressed over deceits it off he does by taking the Universo by midJune the council by individually and as a reason to tantalizing on the rights although you may use 1 of figs or as we say minds when rise of these then it's a set of using this summer lateseason is a society that they make life during 2 6 0 0 and Uganda army southern China knew of what we felt was you didn't mention from
15:46
we're not getting more sense which of course implies only Niranjan transforming between Shiite zeal and the annexing so what other flag has forgotten this from if you assume that you started a prescient faulted the complex and which is bounded note from Morgan but DMX and lots of we've being Jimmy FTD imaging of the exhibition and a few stock is complexities of friend the return of logs it will studying become it was a guarantee fund and symbols for the initial complex so what I find find twofront dossier zeal From complexes which oddball identified all was equivalent of the 2 Christine complex which of simple properties overall orders unconsciously DMX was the other way then
16:47
during so if you any the scene the theory is the fact that this 2 from Dell's on joint offer causing this equivalents between these 2 categories which I just hope so From the Adamson formula you get maps From the composition of the new music competition of the IT majors are you at the as stopped by means of the test takes on a complex to Poland in these areas amorphous sold you find employer is following up on the issue of 2 2 complexes which friable dimension of was global DX the production of the home of always overall as his view of our movement this this
17:39
is not good either so contains as a bottle of Giza comprising the Montgomery GI because it should take no this year the take ever adopting the likes of minors the exit and the formation of ozone to use 1 and this is complex also works of the review and that of the finding you feel that stand in front of course we use the word spotting the noncompliance so I can't
18:10
edition of the perfect complex's so I will give and look over his description was said at the complex is the perfect if there is an opponent of roaring in the scheme and for each open subsets of the governing the virus under profit complex of the module lucky 15 such that our finishes complexity don't twist think that the complex so the president sight of the open is this year off on the specific complaints locally I have complex which can be identified with it in which complexes in the essential and C often does "quotation mark for this instrument is dependent upon some kind of trust of governing with the Museo del it's not so special case is about the perfect complexes of for example rise modules it's the embodies the size and take the guy the profits too and we the knowledge that perfectly in this city that means that they have found resolution related the model year yes but the lack of assistance inside the fortitude image of Hurricane Frances image so we don't using itself the commented that the question hand take on covering this case that perfect complexes the definition of a perfect complex on the site so long as they have so to of admission but again this comes in only the 2nd in next slide so with the because is I would the the index is the birth the category of the .period that is was the perfect complexes unknown is the until the with you said you cannot be stopped decision eyes being here example of the equal forprofit complexity module fall in anything if you assume the conditions for opening all but this will continue that's the people OK so as a consequence
20:29
of finally getting his timing related another
20:35
protestation of deep affection is but again do iterative to as SCO which is of course much easier because you don't have to lift anything is something which already assumed to be the signing of a final toll dimension and Bloomberg did not mention condition can be restricted to awards equivalent to every whose respect lesson to the suspect Elizalde here's father and he
21:02
has a lot to him In this is the 2nd section there the Justice the general which has been put them was segments of the from on the
21:20
other side of the court the so much as they always do goes into as just a PGA National which is defined by you he did put on that idea and x 0 always osmosis scheme as it was in an accident at the close to the south of of very well article for the rest of the world 1 of the by opponents of the measure of the most creative periods this is the year of the contract called for the release of the state Saturday about the about the fate of many homes Louisiana New munitions unity surfactant and political the men with that in mind that there still is the for quality of him is for the time being enough opposition is still and I'm not sure this is essential in fact but if you dig began Robson in any case will have to take convicted begin the hopes of these good results in the southern coast .period problems but did not mention that can be eliminated at the initiative of the music I don't know when I would find a friend from the same we have to fight for you
22:48
folks OK so and we have this notion of deep affection but the 1st to market that isn't doesn't believe so when we suspected clothing notions what happened was close assume that that is the old comics Zia waterways it was a close enough then there are the following description of the 19 made of the total achieved is ridiculous as beginning in this case and in sight of 1 0 0 call you the intersection of the In recent 0 0 that I I can give you is you as a there was a gross of scheme of the final 1990 J. divided 1 the above K was compatible with media was the amount of stock and then the data beadyeyed judging in my case taunted by the end the power of the drug war during the sense of the site there are they taking us the issue and judges in all complicated thing would just be the formal completion of food to only miles I enough this is Nelson made of clay shares in general are few stuff was going say look at Infineon schemes but it's not quite the Koreans which already for that the Senate bill the benefit complex as we find it so that's not a problem with it but I'm concerned Simon different at this the market position of looking at the at the mention of the of the substantially from the universities inside the following year as defined by the genetics module but is Dixon when using the private To infinite Union of stuff from some modules for all the EP coverage of recession short so in finding and explaining cynical that this complex is the only it's as old as you know and you are offered a perfect compressed Monday the perfectly to the wall of the Prophet and his Iowa laughter
24:55
and would another category which only goes deeper do all of the Prophet complexes which originally by Duchesse perfect complexes the military won't want to lose anything right did this narrative of 0 these are all and because the issues which I which I am working on lots 5 Virginia the overall as they do something particularly into account this investors in its problems and the trust of the men was to introduce his creation that what started his creation and to work systematically with physical complain so what I mean by physical demands on when you it is different as in going backing that is there is no assumption of some used to be details about the nest or anything on the recession just enough stocks expression with no particular problem but this is can use to give fistfuls of another user from goes on and and support that the and meeting the new inducing notion of investigators and so on the from doing can think of as a 5th so it's especially by using from Alexei we reserve the physician given by the idea was defines a 0 2 as the been getting profession which is discreetly mission and so I negative and we just a guy called always for all the chief of the fragile Barrett doesn't does matter authorization by the order of the country operators which is increasing frustration where the previous 1 was decreasing but I don't uses this 1 because I'm walking on I want the only 4 questions Monday I so I have to another inflation by making it and support it with a physician DID the precision coming from the base but his description of the decision for ordering the mission to repair finally wants the overall as other mature PGA the Jagdeo which is the governor of the maps to the teenager for its zoo 1 % James not really fear finds you you think we decide you over whom to define a thickening you could stand other futures fell by the divided by walls of decided during the war so where we use of donors official Questar antiquated this notion was encouraged by progress in his new the restorers but that thing that's a few other examples ice module that start throwing a ball fees and interest that inside the politician morphism 1 is fizzled isomorphic that is you have to take into account in the tens of water to the fish vision of the we have the big any professional enterprise and this you fish televison so that you are in the course of categories between physical 11 existing would use for the 5th session of Andy Card previously on the results the story in this stance on works that will work for the confines after so now we have
28:18
to go to the market so there is a need to around to say it's not category of his government use another million category but now that it is an exact adding only in the sense of
28:28
creation and that is you have a Boston of exact sequence this has been investigated by constructed the day after the glories of the exact is the sense of community when the advisers to the category of 6 modules which until today some additional input assumption that the cannot use here but the point is that an order from the and working with you that you have enough encyclical displayed objects torrential in the ability of the user from us that is don't support me on this .period affable entirely with still the 3rd you what you can check that the conditions also To look at around complexes Firestone imaginable breaks and buffer complexes can be extended From with the exposing of using them as geniuses for the context of the government you the 2nd statements so I will use its concession to divide the 5th of signs the front of 6 0 and from now on I will always assumed that they missing respects his question so we got out there will be notion the aggressive of getting only between the dominant the stilt complexes which of 5 fundamental part was equivalent of the eggs To this same thing which is the study and will examine all parts of the world is all previous agreements that no restrictions and you know history can define the category of the traffic featurefilled complexes as default by the local conditions the greater resistance lifting offer a subset of effects on which company freestyle complex and interesting insight comes from the perfect reasoning with perfect that complex underlying addition to go so to those states the limelight I have to know we have to price for the pudding the existing mission in the definition has no evident when you see it so I do not buy it on the eve of a system allowing the Union of 4 or 5 feet of 80 I was calling the sentiment of finite although in and similarly for initially still in endured for the last summer and users of the idea of it I can't use them only the induces pressure so we if things in the Valley of Maduro said that they exist even if there was anything the sort of information that they were applied to social complex another Compaq is exhaustive in the chemical morphism from which is an exact from dozens of calls to the art of getting only 4 of this new scandal from from note after you do it in more freezing the Ocatillo In that area geographical basis existence is wellknown to the fact that moving of the varietals itself and only existing 5th edition Of the statement just north of the border
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no yes it can some cases you have to put the assumptions and Foster for the physician was existence create and maybe even a check when the is misleading and can be done about that so far the point that they using caution OK so let me down to the advisory up to presidential complexes that you know that I know of is domain when you enter the stumbling aid so I have no tradition of evaluating morphism native to I've got which sends bill to under 2 of them that being that I don't like that inside the small freedom which is a few still morphism I animal feed which is induced by you the previous 1 and the amount of Firethorn also adjust and careful and of the OMB I use a lot of them laugh vigilance fire from anything here where is place in a single 7 under to the set of movies and frantic older I'm willing doesn't this month as in enthusiasm Euratom morphism so this year I would call a defiant although not original season for inability to and decision can be extended to the job category to you between the islands by written between the horns so I knew devising complex and eggs although I ask that this is cheating because I'm in no assumptions and so excluded from carrying reacted using complex business is going to be just as total achieved so as to achieve shifted by Dix this is my Dierkes for the official and chief and my 2 lyrics from the Green and then I will use addition in the church although the shares of figs over followed and find although morphisms of fleeing to kill and if I lifting and we didn't myself cherish the composition of 0 on the interest that is and from development dominated by setting Seok transsexual few notes is still the ideal of freedom chest so know if I think
34:27
it is going to be exhaustive
34:30
if they're working out getting Williams that this is going to be equations of morphine and this is my 1st of all a migrant amount and I can involve the 1st smarter than get invited this year
34:41
and there morphism formed doubt do you know checks cherish somewhere in the dirt isn't an exhaustive complex so there is
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amended interim which says 1st on notes which is the perfect when did you have the tougher the complexes in the work from Brighton exhausted Bloomberg in the life sentence than anyone without taking the airforce in fact existing answers isomorphic to judge war printed on them and then the key point in the divided into morphisms you are following don't all into the wall which is due filed because of shortages of the laws existing is to violate a morphism lies in the so you're gonna lose no sane when you go from a complex which is the perfect to its line of the war in science which is just perfect so I
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really find no former indicating the just perfect complex by saying that locally there are presently for falsely need not in this century image of serious chest the Fulton today is an intrinsic to guide decisions which is more business because abundant CFOs
36:00
going so have the following conditions the amnesty qualities adults must be exhausted that is Jewish would be deeper effect and that the minority morphism from the United involved so as a
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career did that get just profit is playing at its subcategory hinted on time equivalent of getting 1 of
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the tougher complex OK you know it's with that section comprising friend of alliance so for the profit and adjust effective complexes can define a single supports mimicking the construction of everything you father arguing in India's 1st of 4 if you assume that thinks or others who was 15 the burden of India for these 2 recessions and modified efficient that I introduced earlier His inside pencil product of the guidance of the DAX 0 With the resident of all acts by the government of Oryx is just 1 example press some new productions so this means that this is going to of DX I was as a spectral on this and other debris could annoying inspect from the production space of 6 0 so we systematically identified the lure of the text with equivalent space an example there then issue tag associated guided module which you can define we could an exact from down the Kandahar after the only a feast of complex the shares this complex which is now complex for in and getting worried that guy on the excellent so we can assertion that current chief 1 x zeal we said :colon mentioned of said Kwesi currently the company said good so you chief on July when Spangler DX which is quite encouraging pretending that it's didn't end of lowered I've use this as a sheaf chiffon it could space despite these you so that
38:23
this case if I were the geographic complex on the southern scientific zeal which comes from perfect complex on the menu and UXO weeding out my excess of his State of the Union of the support of this request agreement she's aged and of going to go for a vote no inside the stocks zeal so that on the upon 115 easy to check and can grew unknowing can O'Brien is to the by taking the support of the new order of the Solar you have this notion of singing simple formula full or if she's
39:11
entitled to shows complex enjoys only defecting to judge the fact that I want to introduce enlistment artistic conditional fees and so the good of face as a complete inventory the because in this case Gordon from the sole issue of more freedom of skins from explored ways you will be 1st and garden square of this morphism with government good comparatorcontrolled space otherwise you all and then from there but the amount was from you .period action from you cause a wise old to start what will otherwise able to justify zeal so this is a classic case of injury on the Durupan being renewed selling Charter always defined on the basis and he said that a 0 is none characteristic fall complexity fine of 1 hopefully the definition to invest images is the actions when think didn't approve not so you have the floor a few of these stimulus support students couldn't of a weekend put back to the time report doesn't mean you can't project to deliver phase of exile on you want is for elections expected to pull back this support the proper and it is was satisfied whenever he always moves so these contained case of 1 of the the major rice was the givers than that of the situation solidarity managers notsonew because it's equal the founded and restricted to the support of the complex and the example is popular OK so no
41:01
political decision of direct investment from tells fold the Madurese ineffable shake of the open door press of the doctrine and that is a complex of when he was unwise there complex of acts and it's a wise is more freedom skins then
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you can define began told as intact as 6 0 all that you have been uncharacteristic triteness Iran's funding Madurese the poll victory centuries and that which is given by a human characters Ezio except that the only was the fact that the ring of the general Bear tells a story that emerged mentioned that makes things at the Museum of abandoned at my disposal here so we have to use what was my answer to Munich's questions communities facility of taking profits and by taking lessons it the final wanted consider this statement inconsistent statements on the cassette inside so fast US images the firm offer Lofton was excusable you have trusted Genoa compatibility following the complex which is longer than the online the loss image of sales zeal of forever .period is a serious example of forever partially covered that up to some recent shift which will come from the definition of affable shake and issue this and the fact that the motion of the definition can just take cookery then find that if you start physical morphism which is an uncharacteristic for if and then as the investment of having dealt with this thing we did affect the next for a
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similar result just offered but have to do something which urging Clinton discussed so far which is used to the increase in doubles 2 of possiblity of interpreting the existence of the on which intelligent and those who do anything as a local around I mean just the mention of the song as the restriction to the subside solution that images from a much nicer on the need to set inside and this is why did user here so with this caveat if you Foster for you have known without initiative compatibility between the inverse image for CIA cherish and in image for the concerns of estimate for the accession of the suggestion of the Duma during those dimensions and
43:56
again as you make them uncharacteristic assumption that the venue of revision of the justifications
44:05
soloist to the case of images Nice trusted case well from the notion of the perfect complex gives way where this is the case of small small fees In this case you love competition between American image of the 2019 marriage of still example and because I know this is a major offer after us the noload you pull this is basically because the 2 sides can be identified with convergence of the things that carefully lifted Sunday misogynistic amongst
44:49
now we did use that the following a few hours most morphism Williams there was none characteristic for complex which is the effect and 6 0 0 you know that this documentary be deep effect when 1 your eyes so this essentially means that you have morphism of schemes which is smooth and you have a complex which I support which is proper so it's an improvement of the classical report on with sufficient when an invisible to be I know a
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few if any officials this vision about the chest you do individually just perfect complexes with magnificent 19 majors so I need denoted
45:36
by isn't the only 1 which is the following that was another problem of between small said schemes and Jimmy F. the complexities in India fell the ANC's then In the delicately woven GOP congressional wives your last year of competition between the 2 studies Cynthia from Poland directly mentioned in the menu 6 . 0 on the dot the sense is the document that inside of the church of the fall of the beginning of this line so
46:15
I have to make an assumption because the issue is rated speed kind of legendary interference soldiers going to screw things in the eyes of office and encouraging and follow the signs to assume that this is a quotient of disintegration going for much that for time I don't think this notion social these conditions should stay for a writer were thinking it was just doing what I had to do to get the right to focusing
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convergence must know that there is no reason why is that from the traditionally which would you generated 200 you should soon assume that there reason reason complex for them but for the time being treated to OK so we haven't
46:59
do you do it this year and then we deduce from this that the state should exert a off problems most left 0 is a morphism between exiled 2 ways you lending banking image of just perfect complexities of residents just perfect complex this includes both the case of clothing and most most maps and Elektra is appalled this is the last of the nation Primos here is the 1st case follows from the fact that and we have these conditions yearend goes for between serious it's you'll cherish on crystalline and if it will have .period In the case of some of my office and his because lower than union of the
47:48
traditional languages crystalline traditional and where the facility ridiculous to assume that you have a proper answer was more feasible small says it will schemes 1st of all there's a trace amount on the argument of the world where do do anything she can exert over as 2 0 1 0 over and which of the 2 years beginning wiser when the
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previously getting wiser 0 otherwise you it is clear from the home place more feasible With this community Fry was Don Virginia tuition and twist and it's not something that is defined soluble bearing between the direct image of a depressant effect complexity .period on the image of its do to casing virus and this the effect is this bearing is a perfect fit for this nowadays you that's the IG Metall the Duchesse profit complex cherish it said just preferred because it's simply that the of the direction in which we have seen only have to be perfect direct images of the notice was small fees for claimants alleging that the yen more didn't you should only
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sold and most stating that the results will converge itself which is former consequence when think was it ought to be respectful the UN Of the previous statement good architecture each person all Newman is very interesting that have a free she thought was Dubuffet complex venue of the prosecution's medical mission in and which was in defining it as a doordie on a at the start the during the war in this way you can define after if you want to make a difference in the going to be the findings in the hope of survival because of people from up by the same taking there is evidence and folded up between walls but this and there job the overarching electoral lost allies lofting the ball person in the border keys still most good but you can define abortion we can do it it's not like some thank you
00:00
Addition
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01:36
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Arithmetic mean
Operator (mathematics)
Isomorphism
Finite set
Dualism
Directed set
Glattheit <Mathematik>
Subtraction
Units of measurement
Condition number
Operations research
Twin prime
Characteristic polynomial
Operator (mathematics)
Algebraic structure
Power (physics)
Equivalence relation
Morphismus
Sheaf (mathematics)
Coefficient
Perfect group
Force
06:59
Taylor series
Differential (mechanical device)
Classical physics
Algebraic structure
Operator (mathematics)
Power (physics)
Category of being
Positional notation
Fluid statics
Field extension
Wellformed formula
Computer animation
Morphismus
Integral domain
Wellformed formula
Canonical ensemble
Sheaf (mathematics)
Isomorphism
Module (mathematics)
Hausdorff dimension
Glattheit <Mathematik>
Module (mathematics)
Category of being
Units of measurement
07:57
Propositional formula
Equivalence relation
Shift operator
Factor analysis
Inclusion map
Funktor
Field extension
Canonical ensemble
Isomorphism
Module (mathematics)
Category of being
Addition
Taylor series
Image resolution
Classical physics
Propositional formula
Functional (mathematics)
Hand fan
Position operator
Category of being
Positional notation
Wellformed formula
Computer animation
Commutator
Morphismus
Module (mathematics)
Abelian category
Fiber (mathematics)
10:05
Finitismus
Curvature
Multiplication sign
Equivalence relation
Rule of inference
Grothendieck topology
Surface of revolution
Morphismus
Thetafunktion
Stress (mechanics)
Object (grammar)
Isomorphism
Hausdorff dimension
Homologiegruppe
Glattheit <Mathematik>
Lie group
Category of being
Associative property
Position operator
Units of measurement
Physical system
Condition number
Addition
Image resolution
Prisoner's dilemma
Forcing (mathematics)
Discrete Fourier transform
Price index
Bilinear form
Category of being
Positional notation
Computer animation
Morphismus
Strategy game
Arithmetic progression
13:15
Group action
Projective plane
Algebraic structure
Heat transfer
Group action
Functional (mathematics)
Cartesian coordinate system
Existence
Grothendieck topology
Funktor
Computer animation
Thermodynamisches System
Morphismus
Oval
Module (mathematics)
Right angle
Fiber (mathematics)
Units of measurement
15:07
Logarithm
Bound state
Propositional formula
Set (mathematics)
Density of states
Position operator
Category of being
Funktor
Wellformed formula
Computer animation
Morphismus
Isomorphism
Order (biology)
Module (mathematics)
Flag
Right angle
Module (mathematics)
Right angle
16:46
Area
Statistical hypothesis testing
Musical ensemble
Product (category theory)
Inverse element
Equivalence relation
Equivalence relation
Category of being
Arithmetic mean
Funktor
Wellformed formula
Computer animation
Morphismus
Wellformed formula
Hausdorff dimension
Isomorphism
Theorem
18:07
Slide rule
Perfect group
Equaliser (mathematics)
Decision theory
Image resolution
Multiplication sign
Covering space
Bound state
Open set
Grothendieck topology
Frequency
Isomorphism
Glattheit <Mathematik>
Descriptive statistics
Condition number
Propositional formula
Price index
Mathematical model
Category of being
Positional notation
Computer animation
Module (mathematics)
Units of measurement
Perfect group
Valuation using multiples
20:31
Sheaf (mathematics)
Dreiecksnetz
Density of states
Discrete element method
Existence
Inflection point
Position operator
Duality (mathematics)
Sign (mathematics)
Computer animation
Hausdorff dimension
Glattheit <Mathematik>
Local ring
Condition number
21:15
Musical ensemble
State of matter
Multiplication sign
1 (number)
Kontraktion <Mathematik>
Complete metric space
Grothendieck topology
Power (physics)
Frequency
Duality (mathematics)
Glattheit <Mathematik>
Module (mathematics)
Local ring
Subtraction
Position operator
Descriptive statistics
Closed set
Infinity
Measurement
Formal power series
Computer animation
Universe (mathematics)
Envelope (mathematics)
Module (mathematics)
Ideal (ethics)
Resultant
24:55
Color confinement
Spacetime
Product (category theory)
12 (number)
Filtration
Perfect group
Ring (mathematics)
Decision theory
Algebraic structure
Water vapor
Frustration
Complete metric space
Infinity
Dreiecksnetz
Equivalence relation
Sequence
Morphismus
Duality (mathematics)
Order (biology)
Funktor
Tensor
Field extension
Operator (mathematics)
Isomorphism
Module (mathematics)
Free group
Category of being
5 (number)
Descriptive statistics
Differential (mechanical device)
Expression
Operator (mathematics)
10 (number)
Category of being
Computer animation
Morphismus
Sheaf (mathematics)
Order (biology)
Natural number
Module (mathematics)
Theorem
Ranking
Abelian category
Fiber (mathematics)
Arithmetic progression
Perfect group
Resultant
28:28
Commutative property
Group action
Filtration
State of matter
Ring (mathematics)
Logarithm
Decision theory
Covering space
Mereology
Subset
19 (number)
Summation
Duality (mathematics)
Order (biology)
Sign (mathematics)
Manysorted logic
Object (grammar)
Oval
Hausdorff dimension
Module (mathematics)
Category of being
Physical system
Area
Process (computing)
Allegory
Basis (linear algebra)
Mass
Category of being
Order (biology)
Buffer solution
Natural number
Module (mathematics)
Condition number
Abelian category
Point (geometry)
Existence
Observational study
Infinity
Equivalence relation
Morphismus
Funktor
Canonical ensemble
Isomorphism
Ideal (ethics)
Right angle
Condition number
Addition
Classical physics
Set (mathematics)
Exact sequence
Computer animation
Morphismus
Sheaf (mathematics)
Pressure
Diagram
Freezing
34:24
Point (geometry)
Image resolution
Ring (mathematics)
Classical physics
Physical law
Line (geometry)
Infinity
Morphismus
Duality (mathematics)
Order (biology)
Computer animation
Morphismus
Canonical ensemble
Isomorphism
Equation
Diagram
Category of being
Perfect group
35:37
Decision theory
Multiplication sign
Propositional formula
Dreiecksnetz
Existence
Equivalence relation
Equivalence relation
Position operator
Morphismus
Duality (mathematics)
Computer animation
Morphismus
Isomorphism
Condition number
Glattheit <Mathematik>
Abelian category
Perfect group
Condition number
Valuation using multiples
36:22
Ocean current
Spacetime
State of matter
Gradient
Sheaf (mathematics)
Affine space
Funktor
Wellformed formula
Produktraum
Finite set
Module (mathematics)
Pairwise comparison
Axiom of choice
Spacetime
Product (category theory)
Equivalence relation
Subset
Voting
Computer animation
Order (biology)
Module (mathematics)
Theorem
Ideal (ethics)
Coherent sheaf
Spectrum (functional analysis)
39:10
Classical physics
Group action
Multiplication sign
Direction (geometry)
Decision theory
Characteristic polynomial
Student's ttest
Open set
Explosion
Morphismus
Goodness of fit
Fiber bundle
Square number
Glattheit <Mathematik>
Spacetime
Proper map
Characteristic polynomial
Projective plane
Interior (topology)
Basis (linear algebra)
Computer animation
Morphismus
Function (mathematics)
Phase transition
Theorem
Condition number
Diagram
41:21
Shift operator
Existence
Characteristic polynomial
Consistency
Lemma (mathematics)
Inverse element
Insertion loss
Ring (mathematics)
Inverse element
Estimator
Morphismus
Computer animation
Morphismus
Meeting/Interview
Isomorphism
Finite set
Module (mathematics)
Glattheit <Mathematik>
Category of being
Fiber (mathematics)
Perfect group
Resultant
Reduction of order
Proof theory
43:56
Computer animation
Morphismus
Lemma (mathematics)
Isomorphism
Inverse element
Homologiegruppe
Glattheit <Mathematik>
Pairwise comparison
Perfect group
Reduction of order
Proof theory
44:48
Group action
Observational study
Valuation (algebra)
Characteristic polynomial
Position operator
Morphismus
Duality (mathematics)
Order (biology)
Funktor
Computer animation
Morphismus
Isomorphism
Quotient
Theorem
Homologiegruppe
Directed set
Glattheit <Mathematik>
Diskreter Bewertungsring
Pairwise comparison
Reduction of order
Proof theory
45:36
Observational study
Multiplication sign
Duality (mathematics)
Order (biology)
Sign (mathematics)
Funktor
Canonical ensemble
Isomorphism
Quotient
Directed set
Glattheit <Mathematik>
Diskreter Bewertungsring
Pairwise comparison
Condition number
Observational study
Proper map
Valuation (algebra)
Line (geometry)
Computer animation
Morphismus
Quotient
Theorem
Right angle
Perfect group
Valuation using multiples
46:40
Perfect group
State of matter
Graph (mathematics)
Multiplication sign
Morphismus
Duality (mathematics)
Order (biology)
Funktor
Quotient
Isomorphism
Directed set
Diskreter Bewertungsring
Glattheit <Mathematik>
Pairwise comparison
Factorization
Condition number
Proof theory
Observational study
Proper map
Density of states
Computer animation
Morphismus
Theorem
Perfect group
Immersion (album)
47:46
Trigonometry
Group action
Proper map
Characteristic polynomial
Direction (geometry)
Iterated function system
Parameter (computer programming)
Cartesian coordinate system
Computer animation
Morphismus
Homologiegruppe
Glattheit <Mathematik>
Perfect group
Curve fitting
49:10
Goodness of fit
Process (computing)
Morphismus
Meeting/Interview
Characteristic polynomial
Survival analysis
Exponential function
Subtraction
Perfect group
Resultant