4,662 reputation
11633
bio website perso.ens-lyon.fr/…
location Lyon, France
age 37
visits member for 4 years, 2 months
seen 2 hours ago
I am a number theorist working in Lyon (France).

7h
asked Linear map with two “incompatible” representations
1d
comment If $G$ is compact, $H \leq G$ open, $V$ an irreducible $H$-rep, is $\text{Ind}_H^G$ semisimple?
The continuity of the action does not imply that V is finite diml.
Jul
13
comment is there a p-adic implicit function theorem?
See page 73 of the latest edition of Serre's book.
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
comment 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
comment 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
comment De Rham cohomology of formal groups
@Jon Beardsley: thank you!
Oct
1
comment $(\varphi, \Gamma)$-modules of finite height
"Since representations that aren't of finite height do exist": take a semistable noncrystalline representation.
Sep
10
comment 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