3/6 Perfectoid Spaces and the Weight-Monodromy Conjecture

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Video in TIB AV-Portal: 3/6 Perfectoid Spaces and the Weight-Monodromy Conjecture

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3/6 Perfectoid Spaces and the Weight-Monodromy Conjecture
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3
Number of Parts
6
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CC Attribution 3.0 Unported:
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2018
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English

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Abstract
We will introduce the notion of perfectoid spaces. The theory can be seen as a kind of rigid geometry of infinite type, and the most important feature is that the theories over (deeply ramified extensions of) Q p and over F p((t)) are equivalent, generalizing to the relative situation a theorem of Fontaine-Wintenberger, and also implying a strong form of Faltings's almost purity theorem. This method of changing the characteristic is then applied to deduce many cases of the weight-monodromy conjecture.
Point (geometry) Area Group action Perfect group Multiplication sign Characteristic polynomial Element (mathematics) Ring (mathematics) Many-sorted logic Logic Oval Ideal (ethics) Körper <Algebra> Series (mathematics) Set theory Descriptive statistics Spectrum (functional analysis) Condition number
Point (geometry) Ocean current Functional (mathematics) Group action Twin prime Sequel Multiplication sign 1 (number) Mereology Element (mathematics) Pi Natural number Reduction of order Square number Energy level Series (mathematics) Extension (kinesiology) Analytic continuation Algebra Condition number Process (computing) Model theory Equivalence relation Field extension Proof theory Category of being Arithmetic mean Film editing Voting Ring (mathematics) Chain Object (grammar)
Point (geometry) Multiplication Potenz <Mathematik> State of matter Prisoner's dilemma Multiplication sign Tournament (medieval) Physical law Infinity Insertion loss Maxima and minima Line (geometry) Complete metric space Element (mathematics) 2 (number) Pi Arithmetic mean Many-sorted logic Well-formed formula Calculation Ideal (ethics) Condition number
Point (geometry) Statistical hypothesis testing State of matter Multiplication sign Direction (geometry) Water vapor Propositional formula Mereology Element (mathematics) Power (physics) Pi Inclusion map Many-sorted logic Ideal (ethics) Lie group Set theory Condition number Standard deviation Octahedron Model theory Commutator Limit (category theory) Proof theory Uniform boundedness principle Ring (mathematics) Universe (mathematics) Order (biology) Game theory
Point (geometry) Classical physics Complex (psychology) Functional (mathematics) Differential (mechanical device) Multiplication sign Direction (geometry) Translation (relic) Similarity (geometry) Mereology Power (physics) Element (mathematics) Subset Pi Many-sorted logic Forest Series (mathematics) Associative property Set theory Descriptive statistics Condition number Injektivität Process (computing) Moment (mathematics) Physical law Model theory Content (media) Limit (category theory) Equivalence relation Uniform boundedness principle Field extension Category of being Arithmetic mean Right angle Musical ensemble Family
Complex (psychology) Extrapolation Multiplication sign Image resolution Model theory Variable (mathematics) Sequence Equivalence relation 10 (number) Product (business) Arithmetic mean Many-sorted logic Reduction of order Object (grammar) Series (mathematics) Resultant
Point (geometry) Complex (psychology) Group action Differential (mechanical device) Multiplication sign Real number Image resolution Insertion loss Mereology Element (mathematics) Group representation Mathematics Many-sorted logic Term (mathematics) Position operator Area Uniqueness quantification Physical law Model theory Content (media) Mortality rate 10 (number) Category of being Ring (mathematics) Summierbarkeit Moving average Object (grammar) Family Identical particles
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if. for. the song. next to prove said. the problem and elements are just a lost art and for this note said it's clear said. a last are contained in the pub on elements because all the parcel from the moment of a star will lie in a star and a stars and deficient bonus subset of our and for the other direction. this year that the x b. paul moment and then fall. that's on the make similar idea its longtime six is top notch new potent. and in particular the sexist some big and such that have sometimes sex appeal to the end will be in a last off or and not enough and this implies that. its longtime six some day in lost over the previous lemon and tense. x. again defines and almost element of a law star and then fix itself as a description of almost elements is the north star or. and sort of know we have to prove that. we have some falling equivalents. the. so in other words we have to see that. the images from the ball which is a tender. the point and so we have to see that. a bar its midst. unique deformations. and for this we use a series of sokoto engine complex. though. some nations which are laid out in the sea was awfully busy and then recall of the bit about school to engine complex. so too. the first in the classical music of arbroath set up some and so to any remorse isn't. r two s. we associate. the so-called quarter engine complex which. is an element of you can consider this an element in the drive to the real of as models whose call knowledge is concentrated in degrees and nothing positive to greece. the and some properties of this are said. of first of the age i guess it's more stunner to use from a logical attention. it's not also sings just. the differentials off as over our. and the for any. i r s t. one gets a triangle. in. dr to have two more use of connecting nor have to get this right. well as a war are. pull back to from his team goes to the cool tension complex from she'll tumor argos to contention complex of tea over as a. i. the.
. and some of this extended. extending the products like sequence of one know some of from for just let me go on. the. and. let me say one word about the construction of this saying so. construction once as follows. we've also someone new to this. and. the first to use of those khan equivalence. saying that. mr roffe could give us more deals with this is a bonus restriction is equivalent to the criteria of some political. s. more deals one of the problems. it. and so instead of to sing in the draft cutting rooms to construct some some fish us more fuel and some way we do this is to choose some. some pleasure. resolution. of s. by free are dross. the meaning just a porno me all draw and possibly infinitely many variables and there is an economical way of doing this if you like and then once sold for. for such important only knowledge was easy to define what see i'm so sick or tension complex should be as should be just one thing i wanted someone extrapolates from this case someone sets sail us over are to be. the simpler this is only the object in. associated two. own. only a one off simply show eligible which then gives us some political a stock more you and your. the timing is right and. a. yes and in the tens or was this was a bit. and. and so why are interested in this it's because of falling serum so. and deflation series so that obvious a module row wearing and i are an ideal such that i swear to zero. and and so said. r. zero to be almost i. and. that s b a flat are not old abroad. and we want to. lift as to have fled. all to grow. and we are asking what the obstruction to doing this is and what are some possible ways of doing this and that's on sept was falling serum. which says that if there is an obstruction class. in. thanks to have the coach engine complex low cost model were on old was where you sit in. the ideal tenants turns up to us not. and. the possible lifts are the tours are under extreme one of the worst same objects and see all to more physicians have one lift our thanks to row of same sex.
i. and in particular for example of c o two engine complex vanishes then there is a unique gift and the sort of there's no ambiguity whatsoever. a. it. and segments the formation results that we will need to said if we had already have s. and as prime two. lead ology bross and we are given a home or film. from the reduction so. on the reductions. two are not and were even have a home office in from that's not just not prime and. was the most are not as ross. and we want to lift this too. i. home office and promised to his prime and then there's a following. that there's an obstruction klaus. in extra worn off. the potential conflicts of this more. over on old was way isn't just not prime and there are not i.
and the possible lifts. foreman toys are on the group and extolled the same. thing again we see the difficult times and complex managed to send also home office seems if too neatly and so. and it would be interesting post temperature in for medical attention complex plan isn't as the following are not propitious. it also appears so i learnt his firm's book of carbon from year old and i don't know whether this was observed before so. there is falling varies quite serious of arson. perfect if the older brother. in the courts engine complex of are over fifty which is.
so long. and you'll need a slight enhanced version of says. so it. but all too as him off isn't. i have a theology ross. that our law foyer the. the already brought. are we as a whole month isn't. because the for the news. and the. as in the same would be defined as five and we assume that. the reds and from us. them. five as of all our is an awesome oath is in between. and even in the drive category between. this and the song it's i saw from the dr sense just mean said. it's was also it's not the most of them and all higher toll terms manage it. and. and then again the court engine complex wishes. k.. and. oh. so for example the first statement. and it. the. can be used to say that. ring a fifth victim so far just a unique. the formation of our to have threatened putin to complete. the p.r. the road just so much closer to home or think about some directors an unusual definition. and. and also some the. it's clear that the. so my got one of our over fifty is zero. why is this so. i think some are and ex-wife to live here. then the aches the food was the peons that's few times something and zero zero and then some of the crucial identity behind this position here. and. and so we just have to like the. go for slightly more enhanced argument and so it goes as follows. so. an. soled shoes. the simplest a resolution. and i and one. i'm so we also have sort of some relative from us. we're all which is a man from off by and there are s. daughter to a start five and the assumption just says that this is a weak opponents are. there's more to do whatever we call it. the. the. and and. so we have. to whether missions. of testify by a free simply show. as for high office. i was wrong. so both sides of this give you such a resolution and so it follows that they both compute the same hotels and complex which means said. our fire tender are. all know if you like. of the cold change and complex of as start over our course as lofty to call attention complex as it is also taught us by. over off five. but on the other hand. we can expect the computer was the das this thing to do on the differentials so the sum of one part of the simply chaudhry broads just some. the internet porn on the audubon general and. then fee s.k. over our. on differentials. that sticks i too excited to the p. which is again zero so paulo census murcia memphis which is causing a small film is also the aromas. the. and particular both sides of his last most of them have to manage it. and this is exactly what you want to. some of the. but some of the same saying just concern from a different point of us to call times in context. it's all wrong. ok now we have to use this wishing of sokoto engine conflicts but first we have to sort of debt to syria to the almost context of this was also done in the book of carbon time you'll soon. i. they show the following that in so if you aren't s. are cannot alter ross. then if you consider. the potential conflicts will fizzle more are but considered the almost way then begins as an object of dr kedgeree know if it's almost one year olds and show that this depends only. on the mall physician. from our way to essay of can almost always ross and soul and you get. i. you get l.a.. they'll be in the driest country real fame on the walls. for any. in. loss isn't. it should be of can almost always rose in this way. and. and in fact the gundam you want to find a sledge we find version of this contention conflicts which actually is an actual model some old an actual ring with the rolling and it's almost worsen and. then the previous serum stage for. syrians bought the formations. stay true. is almost world. and the. we all men need some of the following coal area of this mission of sokoto engine conflicts which is set of a bar is the perfect on it. kaine aunt they all want pilot abroad. then. the coach engine complex. of a bar over the saying to a zero. a. and while going to reduce it to the case that was already handled this sort of. the scene off too. represents. a bar by a flat. i'm not want pile draw are such that of for being is an awesome or prison. from our point to want to repeal was our and. again because the strange elements was simply earned the the someone puts rise this but this doesn't work. lot to this book there is defined as a different way of for presenting a ring boy and actual almost anyone actually so what they call a double or shriek which is to take a loss rate which was. i recall like small ideal tens or an all-star. this moon general be flat or eight is one that's better so the same might not even the flat and but it's not an audit by any more mccain not because does not contain the identity so we ought to officially sort of have to at the identity and of modeled and. and so is this works. them. don't want to get into details here. and i guess one could also just to do the same prove some low or is it possible for. oh no. so. so it.
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