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K3 surfaces over finite fields : insights from complex geometry
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Title  K3 surfaces over finite fields : insights from complex geometry 
Title of Series  A conference in honor of Arthur Ogus on the occasion of his 70th birthday 
Part Number  3 
Number of Parts  12 
Author 
Charles, François

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  10.5446/20238 
Publisher  Institut des Hautes Études Scientifiques (IHÉS) 
Release Date  2015 
Language  English 
Content Metadata
Subject Area  Mathematics 
Abstract  We will describe how insights from the geometry of complex analytic K3 surfaces can be applied to the proofs of Tate and Shioda's conjectures for K3 surfaces over finite fields. 
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08:49
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months its 3rd 3rd OK so the 3 facts In July if mess not only the spread so that we are not thinking enamel as square the during his father smaller so that the book so this providing dash vessels of hobbled Over half of volatility of distortion while whereabouts well if this were a few of them would have well selling implementing changes in condemning tosses and the DeKalb information we didn't in key phrase that will adopt now Wiseman isomorphic that is the continuing item or contestants but that halted check but they all contain adviser responded to southern section that is independent of the choices on the will of all classes and then by some noses of the belong to bond fund but we all over refined feels so there has around 500 give says is the part of speech was bonded value so we have only so we get a contradiction there was no mystery the "quotation mark so I want to explain and and so I want to explain why these things do not have likes so that the people of good of in the 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agreement I was going to do so voluntarily to the of course of course of course but this is 20 within this year all Gates also solicited the wiring the world to is also like I want to give and where they want to explain explains how you can pool I why these 2 5 generalize to defuse not elliptic you know this is a way to give finest all so for fortunately so eventually to within weeks the winning the uh using litigation for the 4 classes in the hall ,comma classes of all hopefully to construct and variety here it was Tulsa and there's interKorean fibration into something else and the 2nd thing is we need them still criteria for prayers at ElBaradei accidentfree all something other than the 2 columns from all would we needed cuts in the form of some kind of ominous from coming along with famine and even steers clear of that ever left his number would come from 2 years continued to weaken the same thing so well what do you do with the Governor Paul while you go inside to many I mean Yukon 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of United another way of saying that is that if you get prison chief you dig up to you can exert politicking you can fully united together .period active while bundled coherent Cheverton ordered to bundle and that's what you get well we don't have the end this is a fact From the farmers here this is your life into a really and your account so there is under the resolve exceed hero but you can answer the phones feared problems in the president is around and maturity speaking Protestantism looking for suitable transplant they are supposed Copper and now includes more than others there will the continuing the thereby mentioned when Donovan didn't go as high as you want it's always that always seemed like thick when a the global section of only get to always generated injected for only know where everyone informed and they are also often beginning this rule over the then this is what you would call home of genetic 94 Nova finds here they don't want to be the definition for all of Central 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the base so the final falling subspecies of this defined as 2 of finance of access to be the following things Oregon some of the greatest 80 fell 0 and the last the welfare and only now OK so it is likely that need to be and the are 2 major injuries and the beginning of of the new in of acts only after this is from the flat "quotation mark this from its use of said OK was 1st known to read 0 2nd thing belongs to reach 2 and the we and on this way in my writing that well it is as you a twisted Southland Christian change on X well this is a space where it started the classes leave the gate to the voice of the right of shift twisted by the castle entrance portion in the middle and the end of this season and to challenges of achieved the I need you to couldn't suitable will lazily face OK so we can we get a doctor to class the event the other speech gave 1 the rank is going but portions of the all day and then and then what "quotation mark it was the director of the University of this phenomenon is also I was be willing to underestimated top I'm in and I'm thinking something like the German giants of air the time has come to the Tucker stands in for human heart to it's you have to put the trend has the right holder for the new knowledge to work so anyway and also the year of the new eligible they wanted only 1 thing so it is not in we will also encounter there indeed the space foreign currency stable Christine she is kind of weird so we the don't called well by is the result
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of a defense quoted above the some EU nations to when then is on the social how they
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get new knowledge of the it's endowed with aquatic form so that we have a quality following instill we had to rank once they see they put them as a hyperbolic again the and just come upon us permission to enter square called euro and the communication creating we 2 of energy Over teapot professions and now this is the October now on the 1 is 1 of the things that don't OK and the square is volunteers then uh and the dimensions of and the need to improve the the square 1 and it is isn't always true and it's too of ending the delegations of Of the yet so everything so I I wanted to set some wonderful suitability because I won't really be careful about the interior and right in in the right has to be put into songs so here is the symbol the superior Teresa Wright has yet and you have to have a lot of unanswered some small things like this it what this is all the remains of the inside page In what is the right solution so that's been around for unless they can example union this year the rank of Nelson and delays the system OK so of the devices OK thank devices that city this and we will use the square was minus to do so I wanted to be and squares holes equals touring too often on their so loser signature
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on the Nelson label is 1 in the Oval minus 1 and there is only 1 was direction Friday 1 was to devise 180 devices at home with it is the data conjectures .period and find them I said so I have found you the Ottoman all the Nelson Riddle of eggs inside each June excuse :colon yeah and incentives to accept really sends a gallant all day long true well we can assume other square kilometer square I wanted to be when because going to be too whatever you choose L solely so that you can fix such a test good yet as prime number I yield to myself to choose Elsa lenses equation in the office and on the nose and we will have a solution there is also an end to the courts this is a good thing it the army to these companies square with you "quotation mark "quotation mark we assume this and then In the end the following things I would have liked to its she's of with rank elderly with I'm director I think but the data and again and again ,comma 0 this is just good score as many as 28 OK gay and that he would the Indian otherwise known as more so this is something you can check for instance might at than those and we would to look at
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this as something which I check and then as if wearing think beach on which uses just 0 euro is often 2 men give and advisers on the Net we square please hundreds of years sold way items commented to that middle middle age but this is exactly without referring to any related vibrations that exactly alternates and situation we don't want a lot of please differently through their mothers amorphous to each other and they all have advisor of positive intersection which is bounded into those of the intervention of the we get a complexion my son as a result OK because I told you that they all need finetuning services with the rise of positive bounded Funds 6 7th compared to lose something waveform of the edited version that you need to feel a little bit of it's so how do you how hungry you hardly make additional syllable of action on at least 2 a well you cannot take and you have to take a view on you can you do the same process but that means thing and then they want to talk with much of 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of the line all means there's a chemical analysis so this has tripled chemical infected and some chemical bundles a lot there is the which is been 219 what because it allows them before this there were doesn't the commerical bungle intervention would dreams big with admitted that gets so you get and find my rational To add plus a friendship so here you have to be of course of the devil because the amply clear singularities so you have to really careful about what you do with the similarities of the rights that you get that's for synthetic variety is regaining agrees on let me go has shown that and are taken care of him and then wealth will begin at 9 million have results of collapse but gives Londoners for a trial has ended the wants of angle that is as good as ample some fixed power about trying you directional labs who 2 right about agreeing that the solid OK case Serbian nationalist things as of its I wanted to do well that's all I know I'm a little bit the than there but the also like missiles also might take away from this 1 in to explain why kind of result that you can't have failed to gather the people this uses his mother and you have to be careful and the money and then you cannot see France's decided to gather simply at the moment but the you fiber through George of the candidates who can make you can pull mountainous land madam overflights what did so in the final and they have I want to give you 1 last the mothers the the Mount in a rational and of history so this is really the saying that the obvious deals is also mandated that sort of comment on the way we can think about but the substance so but recalls overhearing political net thanks misusing argued the service the agency National so I just want to you a :colon result this and I will explain awareness of how you can translate into got OK so orders with it acts the complex freeing understanding project here well then the next well he is a complex right he's over there c acts on the Phantom mobile of 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fighters of the car and I don't misconducts largesse To think about a tool on the fiery political excited and they must petition medical training and and the Journal so generators the price of space so if you this is the quality of the many this is a mess he 1 of the complex political alliance so 5 guns home the movie is from act to lift the siege 1 and told him of the complex manifold monitoring variety please so that is condition Wallstreet 2 Banks to this is the same and asked for guarantees Joan of Will Gold but results In the Syrians injured on is aware of the socalled the 23 overseas we have here that since the formation spacetime 581 we have is complete family of complex cases after it is not something for larger rejected this never algebra and you never for them this not actually never can you never right however it's called this number 5 so the fibers "quotation mark under this consider is absolutely not hold off nite from banks "quotation mark g?aliex to treat and so the size of fibers ice to ride on just a few years the fruits of the novel the fibers off still more features fibers are the 1 With normal bundle 1 1 1 game for the project and doubled Achilles heel is the size of this ,comma trifle is a product the only underlines turn out to be complex curves and his nominal 1 was for 1 a while now if you are major rejected think Well this is a very nice situation I have is threefold I have rational curves in that bundle without global model so this should be rationally connected so this is not the case right because this is not another many fold we don't have any modulation space of rational paralegal having you here the scandal disposal so it's not possible and that fighting to prove that this was speed Russian connected company used its users out to show that's tank well that some fiber I'm sorry some fiber of honeycolored although he has an entire platoon evolving might from scene to well what I want to think that we can do so in effect if candidate To me and I will I want to explain that we can this and other things here and we get a rationally connected space and this is enough to show that it is so used to in the artifice of are that's rationally connected Russian chain connected which is a bit weaker than then we should have been I want give shorts the and his use of the is a world order was a war mission with only 4 years ago official was so this is between image the finest trousseau eggs on a case of singing all this way Georges which they are then denied that all too so the school led by neither such a map of complied or star of new please God they think the the series of events of all so EDF should the government on the ball Nice move Goldstein's was connected components G did so this is how you look at the fall of all global surprising documentaries was pulled by uh often I think that the the form wobble PGA and then this can be added rising away in the standards of this is not just the Folgers in the hole I think what is it now you play with moderate visits to seen as we did before but now you value the ball class according to GAO so for instance has always had a negative vibrations and showing and you marry it it also the and declaration that are part of Friday's G so you get a moving family of forces so get also the kind this is by no means trivial is really the work of initial calls controversial courage on the modest soups and Trabajadores something exists you get eggs 1921 but this morning arrangement all of its forms 12 x this is a wise Virginia they were greatest in Thanjavur anyone "quotation mark now it is owned by a local safaris of youth so as of now we we used to think 1st by with survivors of new OK 3 have potentially good introduction if you want to be Hollywood use the work of the government's model you can who your family acts over a once it so that it has good reduction to dating bobble covers everyone and you can get reductions gets at the bar 41 but the only thing is that this is what we get it all forms of our 53 but the alltime high myself maybe elements of GAM so that the realization that this means that the United Nations probable covered so soldiers and then and there and there none pleasant but agreed the going survival now called some here which place of acts he won 2 thanks "quotation mark so this family history alive after showing the problem office and so they selected this is exactly that it we suspect review had moving family accompanying family of teachers salaries which all itself which turned out to be all formal charter and I have to work well to a universal home yarmulkes and gin joint problem that is covered by its apology the products of the variety and and in a rational and 2 other just want to claim I and I overstayed my time already is that you can using this it's not that hard to prove that the polls based here is rational that's a rational chain connected off has lots of rational curves and during that the to services started with by projecting has lots of Russian so I don't think you can prove it is renew rational that way but you can still improve that its union rules Russian Ching the German you mentioned in the course of their the move was of the University University of research and we have to do this he has although right the resigned over few about this is not using their this the other by the nephew of the late and I knew yeah know document is this is the rank of the job will for introducing let's assume that the conjecture for right Europe at the bar then there's the rank of the animals illegal is is commandment to through the 2nd meeting of the service and the views of the war as a delicate that was here and here WE it is believed that the use of the the I know it's not known in general performance the reason for the "quotation mark by delineating communities has never caught on in the world funding for the vacant electrification people's understanding of the industry has died as the 1st of the vehicle and this is what I mean the stage to allocate 3 and adding to its 2 enemy in varieties the following is a agreement with the report also said that it what the possible numbers while I think you can get any of a number previous winners of the Convention on the Future of this usable insisted the starkness of you do what you want to follow the law it's a little late in the day after the summer home of the leader brave and in the case also I choose to be at the hiding that so so so that you thing that is mountainous should also explain how it is known in artistic 0 but I mean prove a game it is having that acknowledges complaining maybe even win the war but suddenly they religion of their so while there is a traitor to sort of use could study the middleclass thinking and that's not a very weak to to tackle this month results so in a way you you just know that again like a mistake it would not underlined on all consumers nearly all under I mean all these technologies will help so it's a very and in the uses good affect it doesn't use could have you so it's also true that is so that's so funny and you know that you have at least 2 realizes that the 1st rule of the game working out I cystic and eventually affected if you know that you had to the males illegal how we'll varieties too and that's going so let's not completely inconceivable that but there is some nice Street involving Russell forming a softening up to prove it is always the case so I don't know how In other businesses in New York previous through use of Hong Kong the course here this is the end of the no no no incidents or is suspect's although it appeared when in need just a little bit of genetic I mean you know who I think is suited to society's barriers reasonably or something of a variance and much easier to think In view of the Lower East Side the yes I think it is because once you know that lectures and you know the according to so so so you know yeah I think you could be on you have find their full rank coverage to and for the Nelson Resources was drunk as much as he did on the yes but I think once you have the highlight of I think you can get that you have to use probably resulted in people but the IFA New York Tokyo recently while a wellkept is that security had been good for the building so that they got it all works for a Jets histories or peoples to you really rise and fall as long as you want to use could be affected anyway so social so full young Americans through the human but did you also know that they don't want to for people to falls on the 2nd ball of the skin of things what would you like after 5 agencies his uh Hughes's pieties 5 I think but also the need the question the Sosa languages that have been used his instead of using the space and completing to get by with that of most continues its resigns to pull subjectivity of the kidnap and pulled out of chiffon and then to portfolio so that goes on in the comments agent should have some Leon operation as well and so means also my point that going Hutchison I'm the comics case you pull solitude cannot using alliance then you use decisive to pull the public option of hydrogen soulful and where the use of the the of of water and it's all about it inevitably events and so you know that anyway Gomez model is also on something in the Chinese something that is setting but but the user I blind they put the primer of different natures of ones as he used against potential anything reduction or stuff like that but you know you have potential with reductions in the land they like of rightfully so you only part of the world
00:00
Geometry
Surface
Complex (psychology)
Variety (linguistics)
Image resolution
Tournament (medieval)
Multiplication sign
Infinity
Rule of inference
Food energy
Grothendieck topology
Theory
Latent heat
Manysorted logic
Lecture/Conference
Natural number
Ranking
Codomain
Subtraction
Condition number
Covering space
Series (mathematics)
Focus (optics)
Geometry
Process (computing)
Conservation of energy
Surface
Physical law
Complex (psychology)
Curve
Set (mathematics)
Mathematical model
Bilinear form
Exclusive or
Field extension
Computer animation
Right angle
Family
Resultant
Relief
Field (mathematics)
08:48
Musical ensemble
Mass flow rate
Euler angles
Multiplication sign
Sheaf (mathematics)
Insertion loss
Water vapor
Grothendieck topology
Vibration
Sign (mathematics)
Manysorted logic
Oval
Square number
Descriptive statistics
Amenable group
Fiber (mathematics)
Social class
Spacetime
Generating set of a group
Price index
Bilinear form
Functional (mathematics)
Proof theory
Hausdorff dimension
Figurate number
Arithmetic progression
Resultant
Directed graph
Point (geometry)
Maxima and minima
Divisor
Variety (linguistics)
Rule of inference
Wave packet
Number
Power (physics)
Latent heat
Lecture/Conference
Subtraction
Focus (optics)
Surface
Element (mathematics)
Mathematical analysis
Division (mathematics)
Field extension
Network topology
Quotient
Object (grammar)
Family
26:12
Point (geometry)
Axiom of choice
Variety (linguistics)
Image resolution
Sheaf (mathematics)
HurewiczFaserung
Mereology
Perspective (visual)
Rule of inference
Theory
Power (physics)
Number
Sign (mathematics)
Mathematics
Lecture/Conference
Square number
Associative property
Social class
Area
Shift operator
Spacetime
Prisoner's dilemma
Surface
Volume (thermodynamics)
String theory
Bilinear form
Isomorphism
Universe (mathematics)
Film editing
Distortion (mathematics)
36:37
Mathematics
Shift operator
Spacetime
Lecture/Conference
Multiplication sign
Ranking
Right angle
Event horizon
Torsion (mechanics)
Resultant
Social class
Stability theory
41:23
Lecture/Conference
Interior (topology)
Square number
Ranking
Right angle
Hyperbolische Gruppe
Quadratic form
Food energy
44:14
Algebraic curve
Axiom of choice
Complex (psychology)
Group action
Direction (geometry)
Multiplication sign
Range (statistics)
Sheaf (mathematics)
1 (number)
Materialization (paranormal)
Survival analysis
Insertion loss
Water vapor
Solid geometry
Complete metric space
Parameter (computer programming)
Prime number
Weight
Mereology
Vibration
Explosion
Strategy game
Manysorted logic
Meeting/Interview
Oval
Square number
Ranking
Position operator
Fiber (mathematics)
Social class
Covering space
Process (computing)
Product (category theory)
Spacetime
Rational number
Generating set of a group
Complex manifold
Moment (mathematics)
Curve
Bilinear form
Connected space
Arithmetic mean
Lattice (order)
Angle
Hausdorff dimension
Chain
Order (biology)
Equation
Mathematical singularity
Right angle
Resultant
Point (geometry)
Vapor barrier
Divisor
Variety (linguistics)
Civil engineering
Connectivity (graph theory)
Similarity (geometry)
Rule of inference
Event horizon
Number
Power (physics)
Goodness of fit
Fluid
Lecture/Conference
Natural number
Operator (mathematics)
Reduction of order
Energy level
Subtraction
Field (mathematics)
Condition number
Statistical hypothesis testing
Series (mathematics)
Addition
Standard deviation
Forcing (mathematics)
Surface
Element (mathematics)
Projective plane
Physical law
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Bound state
Algebraic structure
Variance
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Incidence algebra
Vector potential
Universe (mathematics)
Waveform
Fiber bundle
Game theory
Object (grammar)
Family
Local ring