4,859 reputation
11735
bio website perso.ens-lyon.fr/…
location Lyon, France
age 38
visits member for 4 years, 11 months
seen 2 days ago
I am a number theorist working in Lyon (France).

Apr
8
awarded  Popular Question
Apr
8
comment Algebraic integer with conjugates on the unit circle
The same is true of $\alpha^k$ and the characteristic polynomials of the $\alpha^k$ have coeffts that are bounded indept of $k$. A lot of them must be equal to each other, so $\alpha^k = \alpha^\ell$ for some $k$ and $\ell$.
Apr
8
answered examples of non-unique factorisation in cyclotomic fields
Mar
1
comment Can an abelian variety/Q have no non-trivial points over Q_sol?
@Pablo sorry, my mistake!
Mar
1
comment Can an abelian variety/Q have no non-trivial points over Q_sol?
By definition, an abelian variety over a field K has a rational point over K, so in your question, you presumably mean a homogenous space for your abelian variety.
Jan
27
comment Number of common solutions of polynomial system
See for instance the introduction to arxiv.org/abs/1408.3224
Jan
27
answered integral p-adic Hodge theory and de Rham representations
Sep
5
revised Openness of finite index subgroups of $\mathrm{GL}_n(\prod O_v)$
added 59 characters in body
Sep
5
answered Openness of finite index subgroups of $\mathrm{GL}_n(\prod O_v)$
Aug
26
awarded  Enlightened
Aug
6
awarded  Custodian
Aug
6
reviewed Reject nontrivial theorems with trivial proofs
Jul
26
comment Linear map with two “incompatible” representations
Very nice, thank you!
Jul
26
accepted Linear map with two “incompatible” representations
Jul
25
asked Linear map with two “incompatible” representations
Jul
24
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.