Merken

The Tamagawa number formula over function fields

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nationwide was on an island sea a role that's what it is exactly the kind of quality years old well on both sides I'm so those who says the following year I was thinking that it would be "quotation mark so I will just as the quality of the world he the well-defined group that states you know this is the most talented can always out the mall he began his mother's holders and quality of bells responsibilities so that so this is what the Siamese so in the world so that the G and expects to welcome conference was indeed on the field and all the PDS support statements from across the jugular could use some of this is to review all right so far the good news you with his Texas sister grows warrants but notably commodities over the years our make no basis and so is the shared everything would allow assigned so it makes sense from 305 in such a way that vanity addresses the various national lied to win the only 1 that so that's what is that during Israel's policy I don't use it to just she is with the prosecutors have have this since its formal verisimilitude is different from schools colleges and some suitable for people you have got to implement fully it's the year of both refused because colleges and which is fall whose son conditional on some some that's what it since the secession aggression holding the causes of this exception is not allergy meaning the virus from that yeah it's going to be all problem is that this is actually the duration of the most users will allow use of original music users will be limited to the was the rest of the ministerial recovery will be eligible for the woman the principles equal his single it was his idea of a table all so that the formula is simple I I find that undesirable side who was in the who mediated on which cost of cynicism in states "quotation mark salutes residents have managed to reduce the majority of the so he was my next year projections report called him business and wounded the head of the organization context which is where you will mean that the holder of the job so here we should on the same as the book colleges and other and the Juergen on next the reason is that the coalition would combine supports this action filed in which also was used during the holidays "quotation mark unit has agreed to assist from and was also at the end and they fall in the she's 2 the of frequently so change instead of just abilities of all she's can evolve as well with meanwhile was eventually brought tens of all but 1 of is what I also so was sensible that followed the duty to take you and you pull back that is about how I was about pollution and like she's better of with these this 1 of the hottest year support albeit 1 of the most days and is the start of the Virginia stories I was and I'm out of his way she was like this is always 1 of the only then was about group of instead as well so here in the future that effectively but I about that the solution because you don't lose focus your you're unbound the Sunnis and suddenly the latter contributed consider the only constructive advice on grounds that it doing so what Italy's argue residual about she's an incomplete so does the want she whom group of the BBC the president yes the dollar because of so it is up to the the delays follow the latest so few modifications Congress as a whole community bring it on government structure so that wanted to work with the help the you leading this is for you and also so this avoided fines also centered on on all of you here the center of structural categories and then beating some sort of political dissidents people would hold a sense of course that forces that worked in the middle of whistle-blowers leader at leaders here as well this was a so you can expect from you is that the city has been feeding the enthusiastic response from the importance well just a set of all the volunteers yes is you have to understand that is table president the region and the you have to distinguish itself from other categories in the proper time on so this is street that enthuses about the honorary the world lotion then the it has been 2 years in a row 1
of those on the floor of the Balkans you can take all their lives chance the government also "quotation mark holes and William Lee deserves it more reasonably goes so this is the last June was headed for business solution and this is not a actual images of the walls will involve about and have made handling Kansas City over in world I was just talking to you guys know only that it was 11 joins the responsible for getting the foregoing the subject of the breed she increased for always already very committed to on the area where individuals so this side of the new minimize to question is you various questions and for but will also get the originals right for it's a little a reduced but media interview with me as long as the so far has to relinquish some of al-Sadr's also confused the value legend is true and also this is that just regard will review the next season it is true that space is very important that we all structures and the columns that support will be a thing isn't it the European yet I'm saying well with Free community of ordinary the image of the politicians on this side I'm the only 1 to compute the Jerusalem started using what she would all because job and then just forget Bialystok lending saying that formula ,comma of assumptions scrupulous Truman offered no reason is completely believable so I like to use this not only is this the reason I it because To make sense of this Council brought only believe Warren Idaho denies the blueberries in case of an axis of finance that of course we find that so the sole movies says she was needs he she uses us will need to have committed all each for OK so interesting was the vote was so I'm trying to help his used it a role usually held the whole of base in support the idea to get you on the always has the highest category because is of this group of people with problems the following is a list you know with all the usual worth about a 3rd stuff it was the result which is supposed to be on the committee that also rose book and she good at it because of forms from the world I told him that she was told that the agency had full political next to a common knowledge that this was our desire is for the whole rest of for local culture From what I have been found to be so the right size for each so you haven't bothered him because each of them is that home the and looking forward to that the fact is that there is a good book I'm very glad are of and although good Americans I think it will work together now as it was known the this still makes sense what we have and the SSA of fighters with the associates to 1 of the key ones and he need developed you know who is at or about the people who are going to get you people to like you members of the the well and there is a lot of the views of the enemy is always the same as the only method of institutional the only thing we knew then most areas from the Union of various of media so good you the answer general some the only 2 for the 1st time in a candidate but that all optional on also settle further agreed that it that many of indeed provided that it is the son a "quotation mark however I also find it so that it will be and with each of the 2 thousand and almost Texas is the new units of so-called Hollywood generally those with national requirements that will not diminish the years from England as well as summer Europe in general and on and on you can them from they said it's not actually occur in general was saying now that I have to go back to the Orangerie connected work on the book and the less will assign another label is always wrong and there's a lot the last thing the at
that time so his a genitals from this is the most prominent and I'm while posing as I always enjoy military and political divide along .period the whole program on CNN as long as we did with that for all the people at the start of the new home breathless as well as horrible accident his 1st of all the middle of this year and the results of the analysis that represents the latest scheme would replace that no word yet because it was the 1 who manages this little scene so what this is not fully all of so the Asian everything that isn't always responded and at the time ,comma finds himself while using sense that I will work and be all the Wallstreet already bungee tools for use as producer was working on the case the the of most of the respective whose services there is something that is going to here none of which is probably the the only 1 that was the leaders the appearance of the leaders of the people in general and World War I will she the other major says she that's because it is not going make it so profitable enlightening what is that the logging industry since the state the ideas for me the company will be related to confirm that the idea that this is the only reasonable that the president of the or was halted the machines with the fervor of operational so what machines what is a longer the the reason for the most part was there you can consider around 200 will see exactly where I have to ask the world over all this so I need to hear the size of this category of peace but for more than news on the cheeks as she pulled out of so he was a priest 1 what is she doing more to reduce use of what approaches level yet indispensable in computing yeah he this makes sense of it I want to on completion of the Africans and capitalism this was the right that and we can easily be used for for the next 2 minutes so you you either finally were alive but it is explained by the military units 1 that has served as a retreat there chief of but it was he what he really want to I will be tested by myself he says that he might specify at all all this us but even so there is an air raid on his hands and that little white light at the end of this lesson is over mesquite is specified she also because this was going to there the battle group citizens strangled his wife and were some of the most as a historic visit to each such you environmental as usual from walls you hands on through this was the best with William and compatibility of all compositions for this performances the but says it has made say state each level of the war workers no 1 was saying that she was with the former who finds the old 1 for although on the she In the newly assertive effortlessly just the problems that have to with the exception we regret because millions of small start-ups most the why was who he commentary on the eastern half of the year and considered the leader of but this is the net so worried that an object on the a wife of the logic wine I want to know what was going on and off he went on to direct their their resulted from this condition just looking at the 1st of a standstill last year you will get out the mission this is the death of his but without reference to a single market were not at all actually but now comes the moment the slaying was actually higher categories because of its role as very bad areas included in France is they want your money could so that we means we use of home furnishings said during during their editors on has also Was it was summoned to meet you much in there is no minds said there was Were whatever categories there aligned to the limits of the although most of the members of the these are the journalist this is a list of Roman here as a single will be in this government brought me and so I don't know I I know that there is a disease in which unions will begin run onto 1 of the solutions to the status of the city so the legal that's not his call for the solicitation was analysts have residential and have a match between the sexes originally metals originally between despondent he's built into the machine as he has in the past all you ask because of people really don't love you won't liturgies for the it USA and does all of
this the son of the plurality of injuries that so on this topic but still you to think that they're going to Florence to to lose the final version of the U.S. there are signs intended by the founders of the world for the full year you this head of state on and just as a matter of allegations that it is the that's true projection was warranted "quotation mark wise use of words and he was told she eloped quality that supports the disease and where all that From the point Huvelle of generals as very good the station but Alaskan Mondays the nation's and listening to quality of that support the liberalizing the destination were in the days when owners have many of them will this age it's the college the violence over the quality of life is the all of but each other the report for his Idaho coaching because relations the changes to the side that lost or we are going viral so we're not taking the colleges there was no closer to watching these between warring parties work mortgages a version of that in the questions conducted in to it all right so little of the this exists for the moment I know it is a follows formerly preventive lotion exists for appliances I just From so why the job as this will get the new elections dismal this year the head of a sovereign lord loads these new models are saying they exit the In the light of anonymous or because of all operator from it was sorry about the Soviet LeBron has rejected all over again or so this part of the wages you can move on from machinists and the number of process we actually from the report is not due to the quality factories but none of which was actually she found out that the government I don't need to the knowledge happened the use all federal agency that is the end of game is reduced has known as or rejected and I would guess that this social variance was quoted in the piece you but I think that at the end of the day Bloomberg is a procedure as very that's named after the founder of the initiative on the part of factory on the city's dispute voted 1 of the most days at the end of the the corresponding as soon as I can and will always be part of the initial states that it is terms of what they all the chief hybrids of munitions b and the sports like me this virus that members the Islamic based on the analysis of it's just that in the modern game you might have you just OK and also to the meeting of the UN leadership parallels the view of the the look at finally so it was at the end of the month of August for all states it the so called them so that we all desire to the findings of the study of the John Deere losing Indiana demonstrating Williams these vessels up cancel arising in originals you must do all you want is for what he has done all states from the start as she Vermont states that the and then there is the home of the origin of course you collagen what is the only thing that exists in our world "quotation mark or what quality is colleges will provide a lot of people like this so actually live in the National collectively known as the next step of the way the buyer you
should go out of the signatories higher yesterday so you move some unit you have to go through and that have it so we have machinery Of the Louis Farrell era is that these that machinery or you know the way to the this 1 said those so we say no to the symbol of your or which have been introduced I was worried that I think will be so the all I can say that he was seated at the back of the back of the pack the plane that both of our show and others have heard of him playing with men is yours but because I have introduced the acknowledges the homology added his goal what is that when we have half of it for the site will hold you in Natalie Cole algebra and therefore is a tool of the United News of the World this is the way we want that to be a whole new meaning that could use the rules in that area so it's soon that is going on in makes revolvers review of the images the original this makes sense what would you say that students aren't that's affecting completion the there yet but it seems that you agree that the 2 are often even the region .period isn't universally during the session the it's time and so on individual local Algerian novelist and all this she also said that in view of the close of both I destiny With the use unprofitable orchid version however is a of each of these has finally it cited national regional and said that the 2 that is not as horrible as it will be a general beautiful recruited you know I don't care to form a new definition of huge we all know that this is a man who metres heat up too so it was a there is no need for worry comes as elders these everyone will have colleges the knowledge about the world around them so each 1 her now co-chairs of the coaches and bungee pollution relations so you have America exercise logic so each 1 of the Internet bodies the you know you have a less formal dress so the a junction for here at world that it was properly used the yet just me a landmark in here and there and I was told that she could always the definition Nunavut is known is that so that there will no celebrated originally set by the difficult which the question what students this will hold political there was this apartments for suitable candidates hold information to tighten its basic issues Istanbul to exceptionally brutal the forces for this book but not the reality of the world except that the occurring and informed the cost of this wouldn't be the same dates in the evenings and involves lots of nominal dimension galas and its rhetoric of reality in which people caught in the new user to service None of question this will agree with me that so injunctions against them over the years and now as they did in Europe but it business is that they said that his ordeal variety you marginalization and now has her energies into an association so that citizens of the world that the mayor and his mortgage and so this is the name of this of all was the regulators because this time roster however the letter-sized followers there as having committed very physically and you really very easily In terms of ecology the leaders of the 2 nations have agreed but they won't say it may prove useful for cauliflowers and included a lot of it was being on the president good food and medicines were previously was good service because only the ,comma based on 1 of the saying but the
statement you like in this long faces generally involved arbitrary throughout the whole of religion Europe so this is the research and quality so I want to have you youthful probably formally takes for his work with members of the so In the face of the various both sides he actually arrived in the form of that is because of racism in restoring muses on the cohomology theories and will use face delivered religious political views on this only in so so here so this is how much time I have been trying to sow and was over executive who is both a father and his fellow researchers at University of Mir there "quotation mark local rural fire service throughout the world and in support of the institute's squabble sunset years have been in the world great it's somewhat inferior to all its services begin formal policy some of our years but this is a business you are not something everyone involved with the development of the there there and this is 1 of the writers analyst initiated the adjusted their PCs to generate view the owner of the the company said we you get so so the user is source so have to realize that led the Raiders you water-related it's actually is a center of resolving the policies and a new study you want to question time and his mind is will formally the last thing is this the from their news show so in a meeting of items as a how improvements but also more diverse group of I don't know if is a little bit of music so low that it says will be assembled from parts of because of the amendments as long as you have there was more to go when he so some and so does not so is is key during the years when users get called upon as long as but stronger we will finally have a more diversified so is the Mosley's face of bundled with Navratilova position and there is no way to get rattled relations plan also rejected most of reform which set a record of the position so that he can result is that the quality because that's what it is what you but that at the day time that the soul but that is what we we call 1 of his radicalization was reduced by overseas revelations is willing to do that is to say that state's rational functions from her with a horrible horrible manageable priests that match the of state rattled off of it in a sense of relief that Russian national revert to the G 2 and G the sensibility actually have little logistical security was all of that is fraught with is what can I do that the state of marched from Florence to do something not all of the portion of the debt is less than that of increased costs and some of the others in the world so I wasn't really thinking about having common policy article In this the national off so that the truth will out along the support border .period England who wanted the division of the largest 1 of those areas it's been shown to them on the phone with schools and out of citizens of media and officials officials said is that a lot of as a result of the rule of review the theft but it is very
important to me is more than you rule but you that did you didn't think so that you do it again the proposal 2 In the course of the year this you you there's remain wary of aggressive on it so that it can be offset by a terrorist part decision just it all on the way to the Carolina Frankel Gold calls during the 1st 3 people and you know all of her actions on Tuesday all so you see it are they being used it was not known but they are also the major on good question this although I haven't spent a year officials I should thanks yeah I do you know "quotation mark euthanasia ,comma government and rule of stop to this season to the next leader maybe you wanted you to bear out the ball at the top of all of you almost all of whom they have the phase of the of the some of those the question is it is a word of the and from that punctured yet universal hostility with these things in the right word yes yes so it's another year so In this unless resolution the so how the budget and would also calls USA and all the pieces of bottles which are the most various single use of the United yet museums involved not very unstable but in general what he said was the news that it is there are some things models and that each year to end the or bottles of souls and they are extensions of the work of our health as the reason that the end of the year and so is the news that there is ample "quotation mark that extensive overseas is and what you think is received and some overs years series so only stars on the basis of houses but she also has funded Union obduracy the world so homework in possession of a form of it's excellent said this is this guy it's all intelligence the unified Union things sight of something from that time on some of the universities with ingenuity is being on board an for all users In fact political the horses and we must find useful here yet but I think this was a very very little but the other questions numerous ways of thinking so was also assuming this was a case of this resolution is this inquiry and its own assessment of developments in the case of the fact that the abundance of Newfoundland Nunavut both of the local people "quotation mark would do the possibility the purpose hearing rights in some of these differences will do gentle sense of this is that there and now that the election included in these conflicts news that it about the dispute which is primarily a little the very of this case so it was said that it is not something that this the In because In under pressure like from whatever but on the other hand after it's all the change of your skin branches in the country also in the it was in the United States in the its assessable business was in about the the cost of the trip over so this is kind of groups policies copies of all our people jailed who is so they're in begin altered 6 outside the U.S. is says section at college change following predators at the 4 of them so no concerning the the mission of learning about it used to this to 1st message here that here the better the world s form that has on here and work here so all "quotation mark and or what is the 1st of the unique to Jamal I think it was the "quotation mark appointed as the also final what In the knowledge that it was and who was once I got as specified generalization he's a register of all as the next without removing the guy with the letter and the Union of so Hi amongst the sciences like John that the amount of assets that is the work the focus of this lovely and this and that is another area where the person is going to be fully stated that there was considering using it to get out of those units opposition a consistently do so we really knew of their understanding of the symbol of the future your name but the final to understand that you are if you like with considers experience they're going to want to have a lot of hard roughly part of the reason growing questions so the will literally will take the final step get exactly the US's planets that years the it it was the finest hour intervals along with the support of both factor as it is the quality of the to the sewer and which is usually in the presence of the jurors reported they it were sold in the this is the nation's most forms of so the find itself certain in envisioned get because factory what is so it's a slow specified 2 have good that was that the well behind this Is it true 3 elements what soon once and for all that the Soviet Union 1 of whom we want them to do would you call that supporters of the rights of our focus to bear it was 1 of the most while this is a book of what do you want them to work out because of the Sobieski ones with all this is "quotation mark tens of "quotation mark so then you you you want to do something which is the American people problem from all over the world although only association's many which turning of election that investigators the data from the statistics yet is book so that the bigger question is what questions 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Punkt
Momentenproblem
Wasserdampftafel
Gruppenkeim
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Zahlenbereich
Mathematik
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Gesetz <Physik>
Gerichteter Graph
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Computeranimation
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Machsches Prinzip
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Dualitätssatz
Zeitzone
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Garbentheorie
Energieerhaltung
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Numerisches Modell
Aggregatzustand
Resultante
Prozess <Physik>
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Sterbeziffer
Momentenproblem
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Bilinearform
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Gerichteter Graph
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Übergang
Algebraische Struktur
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Grundraum
Große Vereinheitlichung
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Benz-Ebene
Zehn
Dimension 6
Tabelle
Physikalischer Effekt
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Reihe
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Menge
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Gruppenkeim
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Raum-Zeit
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Algebraische Struktur
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Einfach zusammenhängender Raum
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Matching <Graphentheorie>
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Stellenring
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Quader
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Term
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Regulator <Mathematik>
Varianz
Nominalskaliertes Merkmal
Analysis
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Beobachtungsstudie
Nichtlinearer Operator
Grothendieck-Topologie
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Mathematik
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Betragsfläche
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Gruppenoperation
Bilinearform
Auflösung <Mathematik>
Division
Kappa-Koeffizient
Polarkoordinaten
Gravitationsgesetz
Grundraum
Beobachtungsstudie
Assoziativgesetz
Erweiterung
Mathematik
Rationale Funktion
Relativitätstheorie
Schlussregel
Fokalpunkt
Uniforme Struktur
Flächeninhalt
Mereologie
Kohomologie
Basisvektor
Faktor <Algebra>
Numerisches Modell

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Titel The Tamagawa number formula over function fields
Serientitel Conférences Paris Pékin Tokyo
Teil 13
Anzahl der Teile 15
Autor Gaitsgory, Dennis
Lizenz CC-Namensnennung 3.0 Unported:
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DOI 10.5446/20482
Herausgeber Institut des Hautes Études Scientifiques (IHÉS)
Erscheinungsjahr 2015
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Mathematik
Abstract Séminaire Paris Pékin Tokyo / Mercredi 17 novembre 2015 Let G be a semi-simple and simply connected group and X an algebraic curve. We consider Bun G(X), the moduli space of G-bundles on X. In their celebrated paper, Atiyah and Bott gave a formula for the cohomology of Bun G, namely H^*(Bun G)=Sym(H *(X)\otimes V), where V is the space of generators for H^* G(pt). When we take our ground field to be a finite field, the Atiyah-Bott formula implies the Tamagawa number conjecture for the function field of X. The caveat here is that the A-B proof uses the interpretation of Bun G as the space of connection forms modulo gauge transformations, and thus only works over complex numbers (but can be extend to any field of characteristic zero). In the talk we will outline an algebro-geometric proof that works over any ground field. As its main geometric ingredient, it uses the fact that the space of rational maps from X to G is homologically contractible. Because of the nature of the latter statement, the proof necessarily uses tools from higher category theory. So, it can be regarded as an example how the latter can be used to prove something concrete: a construction at the level of 2-categories leads to an equality of numbers.

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