Spreadingout of rigidanalytic families and observations on padic Hodge theory
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Spreadingout of rigidanalytic families and observations on padic Hodge theory
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Title 
Spreadingout of rigidanalytic families and observations on padic Hodge theory

Title of Series  
Part Number 
2

Number of Parts 
15

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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. 
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Release Date 
2015

Language 
English

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Abstract 
(Joint work with Brian Conrad.) Let K be a complete rank 1 valued field with ring of integers OK, A an adic noetherian ring and f: A→OK an adic morphism. If g: X→Y is a proper flat morphism between rigid analytic spaces over Kthen locally on Y a flat formal model of gspreads out to a proper flat morphism between formal schemes topologically of finite type over A. As an application one can prove that for proper smooth g and K of characteristic 0, the Hodge to de Rham spectral sequence for g degenerates and the RqgxΩpX/Y are locally free.

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03:34
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20:44
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37:54
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41:08
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58:59
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1:07:05
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our 0 being so this is like the construction of that I find goes where you are you tried to the date of the limited overall result sequences tho you don't assume that enough injectors were lastly if 11 inventing something injectors and you take care of you being became canons 1 of the mostly for before saved as a definition of a lousy 1 of them and they can leave now there and then Golden League also extends the debt cough I would particularly tool complexes but there it is it useful to extend it to the objects so that in the city experiments 2 maybe the primal level policy but the obvious also that you you take you off the formerly endlessly inmate there To inversely minister of In this possessions left exactness no that is the standard construction of such an article from the terrorism balance of length still Chen Kaufman supposedly have an abelian category and the lengths to which I complex Will carries an AIO I want to define 4 the next UNI said I can consider their homes so the loan from the but in I don't the associated he just was a noted that growth in the house when Kewell said something on the double underlining of author so did this there is no other the decidedly exotic so 1 can consider its associated listed there was a now it can't tell now when we woke this fall jets we have deflated Wikinews projected resolutions of the pitiful for objectives that satisfies the hypothesis with dual dual Bob 5 in boats and extol compatible so it is enough is enough objectives and that 1 consequence concerts and in some ways directly and there so I can't find the causes of physicians In closely and then there's 0 there was 0 it would become there are few both to pleasing so the fact that these it projective allows you to verify that left exactness and also it turns out z Z extension tool "quotation mark said the switch from the ability to work with so the firm if I'm given at in June and object of sea and air in the area so I can the rules and the problem of it is the front door of the associated To them the Mofaz and strongly to conveys morphism 2 0 1 0 the push for of sold by General consideration and you never left exact saying this is Paula presentable so only "quotation mark you lose so the fall index is actually represent the will of the ball and it says that the the complex exactly no the yes was a solicitation of the X and Y don't know I just looked at the Gotham big thing there will cry don't know their life here this is a very old friends with I'm not sure if there the generality in but the grow up and going to spend much of this is completely redone in animal model offensive but I'm not sure what the Omega stands for the event we're going to do is just as soon fall you said you know so what is not the point is that given given an element in Culver City and then objects in the Gulf I would get only 1 looks at the problem of making this zeal by mapping some saying this is part of presented universe of something kilometer it could be represented so In this case it is severed the difficult ,comma exist but it is indeed to say that there it is always the equivalent Puljic occur a now there and so anyway so you have the notion of a maximum causing maximum object into narrative profile with the particularly so roughly a maximum his way to a full any the why Overbay want morphism so some objects for which there is always the more at least 1 Lopez and 20 other objects and causing maximum means that after embedding being something you have such a morphism and then the results so so flawed unless the exact a "quotation mark coalfired continually Universal and so on this is equivalent to I was in view he is and only
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some say his weekly called in the there it's what he's done the global threat so the the liberalism of it is from tortillas a Wallstreet too thanks to areas for some attend complex yes OK for some 210 kopecks now Her is so no no so this was made and then I still have the the vessel logic which is what I want attempt to pull related with unless something so it depends on the formation of the formation candidate ideas on the same just from Western control on the set of his new office in classes so so now so the DePaul that they want to look at is the following so I have 6 0 2 2 0 0 0 the same place over In effect fine bears and this is fine and this is sound this a of while physicians and then I want to consider the 1st
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ordered the formation flood the formations us some of the city's finite time also throughout the formations and I want to construct in the formation of all this in this so this is the final similarly to what so now in every session a situation where the idea of diesel data so actually I really usually would it depends on the case but it's usually so 1 can uncannily that assume 1 of 2 survivors condition I that has to be in the cockpit of his context let us they're just work so we have in any case the 5 category over the category of 2 0 modules Bloomberg News was to so so I actually left exact coalfired categories all of the 102 most of the money from time and the problem is a lack is the same as constructing a vessel of it there and soulful gaze I can use that the formation clearly like rosaries book so the idea is to wear so so he'll bear the idea of viruses can no "quotation mark so there so did the fire over up over modular and they are also those diagrams of the rest of the carnival to alters it was a good module so did there so you like to do .period under existing law to 3 0 I get the top post countries such as these diagrams and then ii I have motors after opposition 2 hours the risk is so this is actually
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gonna defoliation problem for days so I I really it's classified so solution testified about something like the story of the political I could go from space they are now the so did is sold to control and there is show visitors of which is better than what individuality and there which is the following the quality of life no this fall to flood the market but isn't we said analyzing complex there are only the wonder of Interpol like this :colon 2 on the symbolic those conditions before they are carried deminers clearance of Erickson threw deep class From research turns out that the this this is not lacking their usual duality TOM which is world of several blunders at the availability and the but we will guard the wearer of opposition taken some of those of it's a twisted statement will this is because our home of some operations on K will clearly but this is actually so there are some generalization of this when you instead of further flooding would increase by In the 1st could you have perfect uh rebounded conflicts on so so this statement this is In some very Jacqueline Rose who founded the connection is this so actually I need not fill in this form of full diagrams fold the stoploss mapping to arrest but actually I have to construct a the but because they want to look at all modules at once in order to identify the answer depends on what 1 wants to do so if 1 wants to To conclude there as amorphous and classes demand can just wanted some excellent 1 applies duties among guests the Home Office to the some of this is followed by lighting and a double blow out of something and using various operations and that the architectural and 1 has to be careful about justifying the that this condiment it is and of course it should hold the well generally besides the amazing complex about I'm not sure what that either deposits it's all units example oxidation evident but then 1 would never to we use very fancy and I context so I'm not but for all purposes usually buildings ever that I think goblets and against the existence of the last of the 4 Asian communities in introduced to this case so anyway so this gives a weekly good conditions on the there article 5 would continue slightly weaker was enough oversaw the formation this is 1 way what is now if I I use a more complicated probably if I use or finite died acknowledges the kind the Cathedral of all those make doubles associative tool logic diagrams is the words Mofaz such still process instead of the a probably this is not yet worked out that if 1 looks out that Honourable disorders info that landed to to have some obligated there isn't 1 pulls directly that too the I want to come forward do is given by which is there no show up so anyway so this is our answer some of the 1st step in the construction that I have to 2 were aware of this kind of good stocks and so did the formation with this is relatively easy once you have the 1st although 1 so again I want to looking so I'm in the same situation as ball it's 0 2 please over and over force of that day in the it of our presentation this is open and flat but they don't assume donors in college because this is just for an intermediate steps and I can consider air and sold the formation which are defined by the condition that the idea the power and of the sun is 0 then I want to Collins to define the similar way venison and sold the formation and actually I want a compatible system of such matters from the formations which have the popularity that they have the kind of sound the Saturday the extent of the there is no dyeing why urgent the the chairman of old tear and
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voters will to follow and this where am useless so
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the idea is that I already be so if Frankenstein and sent the tape and then I'll let the I can look at them now and again of those of us ordered the formation of this now that idea is a square 0 weather can make it's in the sense of the idea to keep the economy from the map 2 0 2 0 clears the ideas and I have a small kind of 1st ordered the the formation of this now and then In when I look at this and the divide by disgruntled idea get something which is potent possibly faster than the original adverse events over the formations said the conduct sensor using the insanity enough to land contracts 0 1 1 consecutive days says that I booklet his so now and no 1 can put all those things together get former scheme and then there are the 1 who uses the operation is the John wanted to bid for falters now I want to explain someone in the few minutes Saskatchewan very briefly that plications to the problem of that is about most of them and limited savings sold the now what is those the in saying the complex case is complex characters fell where faultless people analytics spaces look but now we need some condition the fibers I see that the people in all there is a class they sink or refuse accuse us anyway the Bible by Malone Wallstreet to clear land for whenever 1 a Hodge decomposition extends some will still careless lightly so it includes complete nonpolitical why riders and political III condemnable post most novels abide variety is so unique is so dearly pulled in 69 there so using the absolute chaos so poor that that does she is broken fully and those that done the general and the pool was but it wasn't local situation and they're and their using the comprising this classical call mortgages so here I am very naturally because was suicides electricity in college but in the rigid context but to do it doesn't exist doesn't cut this exhibit 1 all 1 can mimic a accusing unchecked construction so that this strategy like this so if I have canal most of them Sunnis case faces but it will also well in there a day in case I need to work in the context idea that a operations and Quinton Susan flatness lusciously easily classically educated on the case and then and then it didn't care they have enough voters colleague .period salt ponds like American policy was originally the spaces so that the idea is that I want to pull their locker for innocent degeneration so there and they don't point by point the idea is to use a spelling out the comedic to those 2 5 extensions of QP and that day and that the idea is to follow the main seldom when the philosophy too go to locals saying so it now social policies of the Union welcome and there more of we can assume the dates says the field is scary focus countries example but not as you could 6 possibly but it couldn't it could be given as a grant example so now the idea is that they have a constant family Over the years and the given fair warning the suspension 5 also monitors should have the same income mortgages so I can construct a substitute of crystalline colleges of course is being dedicated case but locally in any case local I have been there in often numerics I can embed them In some osmosis finland's over there the base and they can consider the complicated down complex so so soviet a completed in Longview out photos of 4 5 0 4 intersection thick fiber and completed along the intersection then I can consider it said construction from the completed the round complex so as the ultimate injecting work is fine and then I get some candidates for the Keston College of the special fiber so to speak so as to pool but this is like bunker local could announce alliance to pull independence of the company and it if universe most lifting it coincides is the quality of this most is because you can pick this is the only singing the coloring and then the isomorphic saying political out there Duncombe origin it is did the was isomorphic and so they have the same lands and for using this 1 can do do you know that nongovernmental and this is the pools so I "quotation mark so now so this problem was is elected again to bear the cost to essentials as well is a steady like this but assuming this presents us most and there With some even Evanston twisted coefficients of it is so emotional so another question so this is finally there is a lot of innocent civilians here this is 1 and sold there but they're so another statement read from 1 it is about the the most spectral sequence so at the time of the 2 2 now there's a tall
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although smallest although the and black liquor laws the International Committee of failure 1 of the things 2 and in this case is 0 so what happens is that the a tactical knowledge so this is a bit of the technical so the called 1st specified dimension falls and within 4 QPR and so so it's all I've done is Italian defense of spaces so Carroll so it's not the usual would you have to define it in the book now there yeah so did In the course of of this is related to move work Is it ministerial post yeah so unique and want to on what evidence is that there be undergo vanishing sites so what Evans is that it's related to a vanishing cycles of so when you attends always said so 1 result is that it's a related to commercial of the Schiphol plus mode .period resources devising cycle of this whole Beaumont today and give you something which is delivered to finish after Santos and so on get a spectral sequence but 1 doesn't have enough got action to control generation so it could be that there isn't there so 1 doesn't know that the generous of distortion he is here yeah OK but now I think what 1700 to expand so 1 way even knows it is the same that the summit of the sentiment that Uncle mortgages so 1 to the late today stood that uncle mortgages and this is not exactly shows there were none of the state the together so essentially the 1 spreads out there too the over the Q period of this most QPR manager space and 1 as been slumming connection and uncle was filters things any construction some plus local systems and you can't put it back in a single drunken boaters method gives a comparison result is basically the same dimensions did that but I must say that I didn't study this one's own other than another couple is to specialize at some point someone wants another the dimension of this is the same as the mission of the space position as 1 wants to pool their there I'm in the flow stuff is it not please locally constant soulful Darius the idea is to build some kind of Punk'd so for Indonesian carriers so I want to Little fiscal vision is that it would be so I wanted to to follow that gives Texas that's a connected then they standards and would be as onedimensional whose base is given by the fundamental laws of any point and that the programmability not so are perfect that we feel accepted this the looking at the class of the diagonally Nextel sectors which can be defined 1 real 1 really put 1 will find that this is given by something like the Qantas sophomore level of fire and Bettye and blow basis and then run can this spread it out enabled encompassing and find the doors must be a basis in the neighborhood demand .period once you the call day welcome to direct get local consistency and sold to boot from it is a ideas who attends oversold flights over there so we have to pull and lighted all almost bunker regularity In fact so the idea is that the vanishing cycle for this this'll suitable for my mother's I cannot recall but kind of almost coherent comb origin In 1 to almost quit and other 2 full days as the basis for all and the starting point is the case of an nice "quotation mark varieties that I could explicit congressional control the bloodletting and then and so 1 has to find a place not to the point this so did it because this is an ongoing he said he felt he had made to use the definition of what you're looking so but now without knowing that the model is nice died the day there's like this so we have the smallest you can Norris assume that it is that there the model is such that the special is gender is a medically a dose of generically small sedan you'll Yukon 2 of their advising cyclists shaves being differences after Thomas and moderate to these models and small dose and that differentials on this most locals you also know also annually over the idea of a model adopted to the prospective deal is a disease which are locally composition of fire at the time and the rest of the maneuvers and I have all advising site indignities the to and the top 1 is a model of the small doses Omega and this most locals but political to match the double blow out of and which is the donors encompass I get some concerns starting point because this is the it was the beginning of the donors incorrect side get and pocketed directly on the site of a pennant understand this is the top she's going to die of a drug under the noted the amazing complex I that in local killing of F optimistic for this kind of situation of restricted like 5 type in the session coming along well to political fight of composition of such scenes and so this is like the local and I cannot Shalom Cohen was vocalist exposure them and I knew there was a dog always for so to construct smudge then after 1 that defines the penguin is supposed to its advantage so they dares to put it in the nice situation than to put it's nice situation model reflection of final Gould and then to use Duncan's too so that local you have your money and enables where which I have defined at time covered so world which successive they know that fragmentation and all closer designed for the and then A. I have enough all of those so I can the both sides a kind of morally of some kind of common logic and defense I didn't know the exhibitions against Uncle almost automatic suggested red what size but that's sowing sedition won poster of despicable later but In this sense of the world is not going to use this year because of what it was you know this area of the university system in the in the form of a letter from the heart generations you don't know
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where this this when will people get intention companies end up and how there is it a lot of Tokyo's stock I have stock there it is a assess although there the formation of the year out here so I have to construct fence although those of the formation and there a a lot of that over exiled to 2 also I am the begs the overlooked is law so the idea is that they have some single overran OK divided by some ideas that I 1st user stumbled abduction defined by what was that all 5 dive over and over that this reverse with the then I have to To construct successive votes of the formations of the borders as the 1st although 1 and there is a problem that is still it isn't the diverse under the condition that they made is not just in terms of the funk toll of isomorphism classes but the strongest since I II and III can compute their so that there isn't the goal of morphism classes so it's and it's likely find information the is provided by there even a blind would use the extra is likely final information so 1 is that if 1 as this generation's sitting on what it is is receives left exact refinement solid runners some general information on this and this can be useful To call where in some cases depends on the passages users and everyone can use some shape amendments and another presented by Paul objects and so far as I have this week good article 5 of Katanga shares of some objects of this can be used as a tool all the books of the existing although some 1 he is the point at all originally this was just racially turns out that there knowing there it's fibers so the point is annoys fiber is equivalent to dated DeGuerin defined by totem complex and you know and informal office and so anyway suppose you just pull this thing in the butt of garlic them over there that I could think of it is that carrying of higher information to to Darius situation is the object in the best category so it is not given sufficient legal costs while there so what do you want to find a way around the world I think so that their but in the case involves a topless with Over .period coming from died of heart and probably get the only would rise to become a fully formed and is less careful about so many were using these Weekly good notion that can go so it's independence I mean it is we fix in salary but it's the several smaller technical alternatives out of there on of the lessons from for members of the Senate of the questions here on high use the use of the last part of the policies that the incident so do you was that you can prove this generous of hostages last year and values ran all over you have something you can analyze thought about nobody does they dont so I thought about so some time ago I thought about this a jazz out it so that it will follow a front pulls the their dimensions locally constant then I tried to put the measures locally constant by using almost Violet the but I think that's actually like and ordered generation is solved this by using but being kept looking at of these this created the codes although the center of the city the shortest day I think this is I was there I unique among the statements that some of the additional resources with them over the head is now a huge of something like you have to use the law of the land that is of he was listed I want to news Philippine indicators the fuel at source because without looking at the so in any case so I think that the so I think it's what 1 1 way is to accept zip there so to do just that users as a black box that the quality of the mentioned 405 accession of QP and then tried to pull that this gives Immokalee constant shift but using a apart apart that's the beginning of the end of their sources of pushing the letting resolutely resulted in the .period shares and send that I want to related I want to say the on court on the square and tool 2 tooled around there so that this is 1 way to lower than that of the hands the last year I was just saying there still a 2nd right this an inch what