Principle B for de Rham representations
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Title 
Principle B for de Rham representations

Title of Series  
Part Number 
6

Number of Parts 
12

Author 

Contributors 

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  
Publisher 
Institut des Hautes Études Scientifiques (IHÉS)

Release Date 
2015

Language 
English

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Subject Area  
Abstract 
Let X be a smooth connected algebraic variety over a padic field k and let L be a Q p étale local system on X. I will show that if the stalk of L at one point of X, regarded as a padic Galois representation, is de Rham, then the stalk of L at every point of X is de Rham. This is a joint work with Ruochuan Liu.

00:00
Point (geometry)
Musical ensemble
Group action
Variety (linguistics)
Range (statistics)
Frequency
Group representation
Manysorted logic
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Reduction of order
Cuboid
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Hex map
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Covering space
Spacetime
Expression
Physicalism
Set (mathematics)
Cartesian coordinate system
Local Group
Field extension
Proof theory
Category of being
Computer animation
Hausdorff dimension
Right angle
Hydraulic jump
Family
Local ring
06:59
Point (geometry)
Principal ideal
Complex (psychology)
Group action
Variety (linguistics)
Direction (geometry)
Sheaf (mathematics)
Drop (liquid)
Repetition
Open set
Group representation
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Term (mathematics)
HodgeStruktur
Reduction of order
Moving average
Field (mathematics)
Subtraction
Units of measurement
Condition number
Algebraic number field
Physical system
Area
Covering space
Numerical digit
Spacetime
Projective plane
Mathematical model
Mortality rate
Limit (category theory)
Local Group
Flow separation
Arithmetic mean
Vektorraumbündel
Graph coloring
Large eddy simulation
Right angle
Family
Resultant
Local ring
13:53
Point (geometry)
Group action
Connectivity (graph theory)
Skewness
Average
Mereology
Theory
Power (physics)
Summation
Group representation
Frequency
Exclusive or
Lecture/Conference
padische Zahl
Subtraction
Algebraic variety
Physical system
Condition number
Area
Statistical hypothesis testing
Rational number
Process (computing)
Moment (mathematics)
Morley's categoricity theorem
Mathematical model
Limit (category theory)
Connected space
Proof theory
Right angle
Units of measurement
Local ring
21:37
Covering space
Spacetime
Product (category theory)
Element (mathematics)
Curve
Infinity
Complete metric space
Dirac delta function
Local Group
Grothendieck topology
Maxima and minima
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Tower
Quotient
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Right angle
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Fiber (mathematics)
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29:05
Point (geometry)
Group action
Direction (geometry)
Multiplication sign
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Field (mathematics)
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Fiber (mathematics)
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Shift operator
Amsterdam Ordnance Datum
Infinity
Ring (mathematics)
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Arithmetic mean
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Vektorraumbündel
Spring (hydrology)
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Absolute value
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Cycle (graph theory)
Object (grammar)
Pressure
Marginal distribution
38:52
Point (geometry)
Group action
Fundamentalgruppe
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Heat transfer
Student's ttest
Mereology
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Number
Summation
Frequency
Mathematics
Goodness of fit
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Subtraction
Field (mathematics)
Units of measurement
Stability theory
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Topologische Gruppe
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Conservation of energy
Gradient
Expression
Physical law
Moment (mathematics)
Content (media)
Infinity
Mathematical model
Functional (mathematics)
Bilinear form
Category of being
Hausdorff dimension
Universe (mathematics)
Quotient
Module (mathematics)
Dependent and independent variables
Right angle
Fiber bundle
Cohomology
Family
Local ring
Relief
53:41
Group action
Shift operator
Lecture/Conference
Energy level
54:41
Complex (psychology)
Group action
Characteristic polynomial
Water vapor
Parameter (computer programming)
Power (physics)
Lecture/Conference
HodgeStruktur
Physical law
Field (mathematics)
Physical system
Series (mathematics)
Spacetime
Generating set of a group
Forcing (mathematics)
Physical law
Counting
Volume (thermodynamics)
Limit (category theory)
Local Group
Equivalence relation
Voting
Lattice (order)
Dependent and independent variables
Local ring
00:03
so you can I'm around
00:17
thank you very much so I'd like 1st thank organizers for invitation to speak are here so it's a great honor to be in a conference celebrating Mother's birthday and I guess I should apologize at the the beginning that are coming up really In some kind of new to this topic tend problems make mistakes so have expression tricked me into the Leica is like case professor blocked a set of physics is difficult and I think got a clutch there is also difficult for me so I just tried to appreciate the box of gay people it's just the recall the following this did you see that so let's see you start with the tale recoup the financial extensions it's plotted fields and recalled that both are you so rolled in category representation of the Golub group to some data space over chilled it's called the wrong if I ask you consider the following from your 1st because of me 4 Kilkee with the some during carries range the takes the variants latest dimension is the same as the contamination of too OK so all this concept is this notion is important because we know that chaotic representations coming from John train realize that actions that galled by the College of some sort was projected by entering Friday's satisfy his property this is no against this fund is conjecture and proved that various people like the soul of that the situation interesting wearing just body I should say it is a joint request OK so the situation we're interested in is the following 4 supposed X Over cover cases glitziest malls I think connected by Richard ended Brighton so I could start was a direct right about the invention if I need to go to the end and the geometry of and start from here at the beginning so that the music supposed health what is the insecure she or maybe that's the safest for something like this and nothing like this in the local custom In fact I think all of system and suppose for it so if you're given fine extension cable and the points on the variety see then you can consider the stock of this fall of of this a local system so that the stock is really can be considering you probably want to consider that of Jim Mitchell stock over to match .period and then the stock is going to be a representation of the call look it's the it's going to be a category representation so here's the explained the the government will since but the thing so far this there is is following it fall some points 1 .period the text itself had prior to the start known as the wife of to the start of in the fall every .period that is why you some fine extensions could be some of the its Oregon Sonics namely over any classic .period the the crisp instructor OK so use the inventor of the proof is really simple but that the this fake 1st make a few remarks aimed at giving application before explains the idea so let's start with the remark In the 1st remark this again asked the same question if you replace come christening but didn't of course is not correct like this defended the family of Friday's at most and that has put the reduction and someone this similar to my reduction efforts and pledged utilize Alaska the Hodge take version and I assure I guess it's a 4th but and no 1 country can OK all the SingleA so this is the situation you
07:01
can't think about that was that I I don't know I mean we should be assured that the thing but the wetlands I just understand what is the drop so far so good OK maybe later I of directive understand was sophisticated killer the review OK so the Lucinda that is missing in this LOU came thing about it's a family of folk adding representations parametrized by a right by the variety acts so you usually called like merchant family but there is another noting 1st which is important in style and color it is good at arithmetical family of getting representations nominee in that situation is that it instead of having a look at how local system of writers who consider are there Zagallo representation of got that color Group acting unit vector bundle on summer are rigid analytic space means that situation I think this is the the stories complete different and I think it's like so problem therefore clearly so I think it is situation off I invite new correctly it approved by by up agenda ,comma set this apart from Locus is a closed South yes I think so ,comma some is closed under some conditions analytically closed so so it's very different from the surge emissions situation where you just required the reps mission to be Brown at 1 point he gets the Brahmins everywhere so once I think 1 should the ruling of compare this with this please do not much of the really compare this with so this is a result of the name which equaled the 4 principal B of the opening of the title which 6 of the following so it's supposed to have other effects over as Islamic midseason was proper prospering it also that of involvement of complex right here and as soon as commented Oh ,comma exaggerated In the Still of all known if they have a family and the family of Hodge plan the fastest I checked the book with this entirely on the lower section come on it's globalization of some shared on as this sentence which is should be horizontal with those men collection now if he had the last word in on the area ,comma reviews of its family of parched last term interest by as well as a means of globalization of of something of was his own for boss who having its a rating the bulk of units will use the introduction is needs a little bit complicated I need to led the rum call ,comma maintenance so that the digitization of our world our yet and the there's at the wrong continent but that you may was woman at the Apollo compliments to the of nearest yeah as is absolute Hodge at 1 point it is every bit as this absent at so this is what he called the principal being which gives us such as the title some talk OK so me before being the need to explain them a plications that there are in fact also the motivation of the of the health of SIS work let's start the let's consider GE a reductive group and acts as family of like Hodge structure was due it was just certain limits visibility several covers certain provisions image domains the attaching it to you have and that's the case then Open Contact Group of final deals when you get to the Shariah right which is like entered the label its aquatic projected variety Wis a state of complex .period the points are testing by the public was closed to public auction but there are the the of canonical models says that if effect is a closet projective righted defined over some number field "quotation mark to the reflects field the cleaning out there going to be help adjusted their such now it's
13:53
up to to the limits of our assumption it's assumed let's if the chill .period centered Is this discreet and it is a technical something the company is the final details With this assumption OK I suppose I have of V is a rational representation as of June no then that I get effective Our baby local system on this complex variety just as social construction of G8 GQ acts on this matter persuasive and the future construction and the fact the theory test because you In what do you get the answer it's public assistance until you get the road Apollo consistent did
15:05
you think of power is defined oversupply to distance I know what it was the 1st to use viewers to kill kill key so if explained this it's a joke interlopers fixing on assurances that been Case said this is the reason aggression arts and different rituals such as rational duration and you specify some to talk about the a courses 2 the case silver Over a this is this is the set up the it's Jenna theory on of the canonical model gives such things and the the the the the the the Colarusso however is fact for the race the completed final exclusion into component of the window then the critical only the stock Is it needs a call option vision of global for S is thrown the people so this economy the collaring the proof is that someone of some of the mission but cry when that infected because of the strong right in there is that something very special .period close spatial points you can't shake so the crisp Monday at a local system is strong there as as to the King Kitsap everything so off I should say this but being there's the remark Is this very this cholera is not assistant is not physician Robert selected is if this is some special connection were consumerrelated memories this is this is unknown USA I guess so GX piece of of any type process conditions because use this situation it is no disgrace punishing rough writing just parametrized parent has certain of motives and some motive is appearing of any and that this local systems are just the local is of the categorization of his and the mayor of the Nunavut are amended this is anticult approves the collar the amused by was fast suggestion of Kevin so so this Nova Shimer writers of opinion types but it's not knowing general because suffered general shimmering is mean it's expected to confront the name that this summer writers should should apologize motives but we haven't In generally don't know where to find the motive but nevertheless we note that the padic representation of Jack the realization should be drowned so maybe at 1 day maybe we could from process found him at the conjecture before finding the motives we get there fulfilling the OK so that an amendment in the national however not all of have something this was in effect on so OK so anyway that is 1 of those is used in the home How do we get so narrowly as to that I some conditioning affecting not ever week be it's some of the really attached to a yet so I don't that in some countries not every recipe you this interesting new the only for sound region but now it's I feel that our areas of the devil and yet every moment late but and I want to make this assumption I could listen her show .period of center's Discrete 1 can relax this condition that it's not for for everyone the but I mean as Brazilianmade descendant deconstruct the local system on the shore and their requires nothing of fraud not for every representation and construct OK so anyway so this is what I mean is the whole idea is trying to get to what In every you would expect like for example tried to construct additional costs this connection arrived without defining the motive OK so I think that's the introductory part of the talks President Park from 9 1 2 gave to some of the ideas some idea of the proof which you see and he's in the process Europe falls short you will serve only to find that I think it's a concern locally is using this as you see this wrote a local as I said it's a local salmon sold locally To have received letters and images docket Flynn knew so that the 2 ingredients needed in our this this proved so it was the first one the 1st month we need to do this so that a recent lichen this pro at all college and the rigid
21:40
and right in the period sheets introduced by British shout so loud so now assume over cases most we the curve I just want to prove that they alike can assume Lexus curve but you can't just see the notation so then the may introduce a few more look locations so I need to change and we kiss case a segment of the words of 1 until we choose compatible and then you need gives users element of In some of the flares words case itself I guess I just before the union of 1 of the ticket that accompanies OK so I was in need of a new the map from the PRI itself besides we went from the reports said Our which appeared yesterday so a typical all object objects here then just to the picture is the following so I came it can consider yield some open impulses that sent him to take a lot of poor accordingly have substantial Torres accused of he was the worst of the universe and I have this tolerance the financial covers and the answer this projected limited phone and email the buyer to infinity ahead and just take the fiber so this is like this system is effective gives you a of this is so Poland in the final opponent gives you an object in the known universe product of sites which has been derided as a ceasefire in the past and that went under the and case so that the Infiniti the infinitive in last season you take the Lamont and complete in inventories and beneath a plastic cover sheet to the standard but that we want consider the the dollar tower so we get I'm gonna discover group some of the next matters comes to so the quotient is so there's too many things but galore group and the have heaviest emissions which is isomorphic to the please 1 it was a generator that I got my exercise against the 1 over chicken and this the attempted the king and here I was in the 2nd coming of the that OK so this is a basic sit up and I was so we see no this weekend Pariseau are what we need is a truism some purity Shiv Sunder space so we have you know what we really need this OK so made things Lim Chai right is located near right cloak and India growth should all X plus countries on the private side which is just a pullback in approach she found X tall and it's a complete genetic complete conversion investment this is good so ah but we really need is a new and of course coarsening the rational version is just the commander of the complete people who need this important puree should all be brought I mean appears people would like follow shelves notation Our so it's defined as follows a meeting of yeah maybe just give you the 15 nation so I have 1st let him be which is which is necessary and act
28:13
appeared yesterday spoke against incorrectly solar than this albeit with principal except persons whom this which make up next to the police hat so I mean because of this and I could start from entering situation but here because this competition and to have to go to the and features so entered them over the ground last protested the completion was with respect to this matter so and and and and then you will the
29:07
old people opening around class impotently again with the usual so I this is complicated but there are many just tell you what I really need and this is the something could complicated so that's what I need is the following some properties sold for but Internacional dormant if at all at margins because all being phased all its so the 2nd properties there exists a filtration given by the nutrition by the kernel did not so there's a filtration 1 you such that if you are restrict I general it's it's a a hard to describe this should been accepted it but the week if we passed through some object in the pride of the on new Infiniti had used the indeed we do have a sum descriptions soul girls I will be dramas can of poets had new restrict to using a in Prince Fielder and adjoint variable here the this huge universe a lot of fun please that take a yesterday I have time for while I mean this as it that I really comes from the action of the arithmetical site and its consumers cycle character so that you if you'd just the chicks and the finishing the GOP then the the guy laughter and tears domestically to keep us or Exxon we have to be constantly or soap and other than important thing I need is there exists the connection almost all so OK so this is why I sold in our so what does mean mean means but role related news that there exists collection is a problem should put it there and then send them right them meaning there is a man from told the ground fault the ground controllers for me the facts so only dikes which is just that the pullback of the usual she from the past applicants on his own now really the comes from from the following 2 propositions Proposition 1 if I consider EIA which is the kind direct pressure drive to push forward of park with she's all by the way if I had the Apollo system my X I can't pull back to its protocol to local system there so I if I just do this push for forward this effective the proposition true if you consider that stalk a means of sorry fiber and 1 .period Mitzi expert agrees to thinks this is the exactly as it considers a bit shy it's a local knowledge of this field so far since the turn of the soul in income won't allow him to get this to properly it with implies a Sarah because then you get a better violates it's the rank and was the crater the rank Randy's craft everything so are so effective tool all approved Proposition to me I just needed you 0 in proper vision to whether to provide the unit that is all of the eyes improper which was just consider you still you there is not enough but that has proved so we need to prove this vector bundle those the cruise hub of the region because it has a connection coming from the connection on old the Doron said so the rodeo bundle with the connection Intercable connected connection is inarguable connection so to prove a metabolic new dozens of political hearing shift so that's all I think the may observations 1 of the 1st half of the finest it's a fine in problem to prove some shade which is a priority of fugitives huge ring and destroyed covers huge copper but that is what you get to something is finite but the anyway what so if you look at it whether you really another with if you from now are few local system you get the vector bundle is connection so it's it's kind of a rumor over things but that will mean probably saved me and not have the correct rank contender but the Vitez triggering at 1 point the so it's basically the room over OK so what I really need to the last I of hope this 2 of the original this is the of you shows you know that which lines I don't care 1 I guess knowledge so so I really need to prove physical on I'm not difficult but the yeah I mean but if I have time and movement of common but the key crucial things through official so so yeah probably like of all the drama is much larger than the drama at the beginning so you need to do something To but OK so so to prove that the Calera of it's really a local statement so I became a consumer Michael exists I mean I consume exist like this this is my spring no it's so still Linda is a starting point in holding the hope candidates some directed image so that new starting point is that this really exists and I of business of like this perfect toys appears you 1st so that if you'd just have that are by the eyes drive to push forward when you analyst at you which is near this is a really can be calculated like the symbolic along otherwise you don't know how to calculate anything that you just so I mean
38:25
this really valves from I guess so this is implied while because there no higher come on when you restricted Rich restrictive she to also invented we restrict consumer some of of the
38:53
original of you all right use this time it is the highest homeowners who goes on to say that I was going to do is to use the right of the people not only about 1 owners and consider our universe that volatility you have Bloomberg this is the use of the law the I former head of the family and his supervisor right inside those are the things that I signed the students the value of stock in Hong Kong and use actually used to be something that is I think I ever learned that proves the righthand side the the scene I think I out just I guess I should approve the righthand side of the ship directly OK so OK so now I want to With individual OK so so really I wanted to show the following so this is each time hoping Toronto the head if I neither the module and the compatible with a top is incompatible with this change it is it's just that go with it and you yes this is what I'm this is what I mean OK yeah still I or I came of so but the vision of With a a published change even the chip is a modeling Tenzer wisdom they over the but there's a wispy over a became so on get hold of them the like yes fled this fall follows from them but you Bloomberg Television plans on hold but this is here is because Intelbased just to help it OK so are right so now I use the fact that there's a really was the filtration on the streets of what I really need to show is that after I think that was gradient I did what I want and that is the ecological fur a social good if those that it just write about what I really want is this guy 2 1 stage the family under the girl I think I think conservatives helped greatly growth J. different this is a finite amount of compatible with this change and manager the end of June was marginal most of the visitors only rooms and handed over to him and I think there should be a to will prove flood that I mean I didn't know it so you know this guy with them may not be Rodale this category Griffis transfers to get what you get the difference as far from his transfers OK so this is what I want so the problem is how to calculate this but the Limoges remind you that we just that denotes bemused right and continued to act as a very good this shit the community within the head right which "quotation mark according to this expression so what do you really wanna calculates that this without relief this guy is really just to China ,comma amendment and to the 1 looking so so here comes the 2nd the ingredients but kept the bits of the new health costs and to assist yes of course OK so here's the the main ingredient I need let 1st formulated a unit of United In a way that the I in the during the work of folk at liability but then I would bet I explained that number was in another .period sold so here is that there and so forth sufficiently Mississippi the 1st sufficiently March there is a finite projected they are long sub so so I guess remind you ate only suggests the real functions on you and said in such steps stable under the action no
46:24
on 1 and induces this this is gone my career and personal enter the I gone on the quotient this year falling OK so this is a statement that we use Bellamy explained Dana enough in another way in which more kind of hard this the 2 thirds and you of all they fear that this allwhite gages of the children use usually used by people who on the use of all schools where be used please this year's no so is legend of the the filtration on years I just wrote we should follow the yes yes but I take yet but when you take a T universe it becomes this it to you it is this we have just I mean it said that in was in the interests of paper father the union worked we did you take the future Zambia above all be proud of all be drunk class according to the colonel filtration leeway after hitting birds she did something Niger yeah yes yeah that's something so Pariseau the new and old I minutes this To me so I can make a huge effort the point is that effect of this the fear and this part of the most stringent in this barracks and think Respondent is forced to consider but for it but also grows so so what's many just understanding that content so the all I can because this question the locals can you assumed L this is a new I star was of the view local system school so this is small which means L model stampede to offer if the trivial form part of the explained its funds OK so you this situation what the effect would be wealth of having a dozen rolling the very symbol part of that increase funding those imposed some some respondents which sits on the fact that there exists a unique and finite projected take the module With the and the action 2 of the dramatic fundamental groups such that has helped invent size and both I want the definitive come to merge the crown and the new editions of the Cold War the college the Chinese of garlic general on faces imprisonment China ,comma much of come and included this is just worried but I would never be used against Member basic version and aren't so basically if you just take a minute adjustment take the log of that gives you the Higgs field the hike if the bank me ignores the tape placed so that so that served us instant respondents and at this stage insisted that none of them a Hicks cohomology who takes school modules to calculate the collar ,comma here so this is something you need to soak up their fault what to you use so so the New viewing reduced known 1 can show if you just consider look they of ,comma Dumitru Jim Ong and had infinitives of this deep so now I can't ignore the Osika ,comma character of the moment this is gonna be there's a map of MKV and members of the item of this 1 can show this season I don't really want I want to calculate a child this guy which is all it's good deeds becomes a smaller and much smaller England so OK so now the dimensions fundamental group could damaging immediate release and was just that a topological group generated by 1 amendment and ,comma sold are Newark from you just do the following them up I have been just below the following landmark From the Nile Toronto which is good exercise so so let them you may kill the 1st place With the regard myself but more fizzle good you have this so right and generous think variants of space to the Justice and that's that the government's 1 feral for some and not enough just a generous cyberspace spaces swung
53:41
1 that you see what do you get is following the lead off yet and that many considered define actions ,comma actor an agile variable the it's just days before and and coastal town tend to be passed 1 of this kind OK so so it's just as a prop
54:12
to actions ways on land once anchovy with ,comma acts by shift so busy that the outright access recent levels Frank the got my variants of this guy is just and generous thing parents and that the and close and generalized that although
54:41
space generous space that ,comma calling Inc this referring to the also are it's 0 pocketful landing
55:00
middling exercising in so now but what I really need this the following simple but crucial observation and case this is new generation this Clinton so you can know apply the vote count by this limit to the situation is because you this guy would be just and came before I there'll be a 0 2 5 because Europe needs to reduce reduced the certain power local knowledge of the arithmetical of group which is kind of the finest it's kind of easy dear so this Lamar I think this is interesting is Rodie equivalent to the Higgs field interest his new we really given input Hicks field but that this is not something not really quite surprising nominee already in the pellets and was the systems and responses of a local fishermen gives you had failed but now my local system Elway's not the just the local system on X kept OK it's really a local city defined over this it's weird little case so there's action arithmetical local so that full invective for this the Higgs field this new :colon basically you just checked because of you many of a generator here is don't have because of this still telling you please change the case as a method to deal with in the case the comes from arithmetical group of what local system of X little case this would of force this mr OK with this text field that is isomorphic to both Joe Turner the meeting might plus or minus I can "quotation mark then is a characteristic polynomial the Higgs field must be and it was a clear vision of the characteristic polynomial had filled must Spanish isn't important so this is exactly the old classic approved by Lexington when he proves if a local system support the complex narration Hodge structure it's a matter of listen that it of In the end on dates Our my wife but more often in the days ahead as soon as it was just as he was told us should have hundreds law which is also on the using and the need for a year and that he would have had their homes destroyed the hold local systems throughout the year before she was the only if we take it out maybe I don't know you may be a little by that and I just wondered adding that news effect that if the local system Rowley comes of Medicaid the Hicksville this new and will vote the get out of the water volume for women among them along the along the decisive according to the provisions of the series In other news agencies in and so OK I guess that from here you get this and it's itself the wrist argument is that it's not new and think promised stop here all you have to do it was the 1st the more I mean it's not the real thing terrible newly passed to a UN which is the really good for something which is more it would have been and me