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Jul
13 |
comment |
Power series defined by Witt vectors / Teichmüller representatives of p-adics
... "Quiconque s’est intéressé aux corps locaux sait bien qu’une extension très ramifiée du corps $Q_p$ des nombres $p$-adiques ressemble à s’y méprendre à un corps de séries formelles à coefficients dans son corps résiduel. C’est sans doute Marc Krasner qui a tenté le premier de formuler ce phénomène abondamment utilisé depuis en théorie de Hodge p-adique [...]" (Fontaine, Bourbaki 1057). |
Jul
13 |
comment |
Power series defined by Witt vectors / Teichmüller representatives of p-adics
If you take $K$ to be ramified and play the same game, then as you increase the ramification, your two fields are "more and more isomorphic". This observation of Krasner is the basis for the theory of the "field of norms" and more recently the theory of "perfectoid spaces". Here is what Fontaine says about this in his recent Bourbaki exposé... |
Jul
13 |
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What is the lowest-weight non-cyclotomic Galois representation in $\overline{\mathcal M}_{g,n}$?
I think that Gaëtan Chenevier is thinking about these things as well, you could ask him directly. |
May
2 |
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How to correct an error in a submitted paper?
Same here - I recently had a paper rejected on the basis of three reports, one of which was a very angry report which was not based on the version of the paper that I'd sent to the journal. My paper, however, stayed rejected after this was pointed out :-( |
Apr
30 |
awarded | Yearling |
Apr
17 |
answered | Reference for $p$-adic Hodge theory with coefficients |
Feb
27 |
answered | injective implies completion injective? |
Feb
6 |
comment |
Status of local Langlands conjecture over positive characteristic
Laumon pas Laumont! |
Jan
24 |
answered | Text for Algebraic Number Theory |
Dec
18 |
revised |
Psi operator on Phi-Gamma modules
added 325 characters in body |
Dec
18 |
answered | Psi operator on Phi-Gamma modules |
Dec
7 |
awarded | Nice Answer |
Nov
26 |
comment |
maximal abelian extension of quadratic extension of $\mathbb Q_p$
You can always take $f(T)=\pi T + T^q$ where $\pi$ is a uniformizer and $q$ is the cardinality of the residue field. Any power series satisfying the conditions that you wrote will do. |
Oct
16 |
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De Rham cohomology of formal groups
@Jon Beardsley: thank you! |
Oct
1 |
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$(\varphi, \Gamma)$-modules of finite height
"Since representations that aren't of finite height do exist": take a semistable noncrystalline representation. |
Sep
10 |
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Why does $H^i(X_{ét},\mathbb{Q}_p)$ have a Hodge-Tate structure?
As Keerthi pointed out, it's after you tensor by Cp that the powers of the cyclo char appear. But a statement like that is true for any Galois repn V by Sen's theory. What is specific to the étale cohomology is that it's integer powers of the cyclo char that appear. This is where you use the geometric input. As to why this is so... |
Aug
28 |
awarded | Nice Answer |
Aug
28 |
answered | What is the classification of characters in $p$-adic Hodge theory? |
Aug
27 |
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$(\varphi, \Gamma)$-module of dimension 2 modulo $p$
"Finite height" does mean that in some basis, there are no denominators. This does not imply the same property holds in your favorite basis :) |
Aug
26 |
answered | $(\varphi, \Gamma)$-module of dimension 2 modulo $p$ |