bio | website | perso.ens-lyon.fr/… |
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location | Lyon, France | |
age | 37 | |
visits | member for | 4 years, 7 months |
seen | 9 hours ago | |
stats | profile views | 2,969 |
I am a number theorist working in Lyon (France).
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 |
Aug 28 |
answered | What is the classification of characters in $p$-adic Hodge theory? |
Aug 27 |
comment |
$(\varphi, \Gamma)$-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 $p$ |
Aug 2 |
answered | Generalization of Kummer isomorphism? |
Jul 31 |
awarded | Nice Answer |
Jul 30 |
awarded | Popular Question |
Jul 25 |
answered | Research-level mathematical bookstores |
Jul 9 |
comment |
Cyclotomic extension of p-adic fields
Oh ok, thank you for the clarification! |
Jul 9 |
comment |
Cyclotomic extension of p-adic fields
@Larsson: "Typical"? :-( See math.u-psud.fr/~biblio/pub/2000/abs/ppo2000_24.html for the preprint version of Fontaine's paper, and see mathoverflow.net/questions/96257/… concerning the availability of Asterisque. |
Jul 8 |
comment |
Cyclotomic extension of p-adic fields
What do you mean "what can be said"? If you add the $p^n$-th roots of $1$ for all $n$, (and not just the $p$-th roots as in your question) you get an extension whose Galois group is an open subgroup of $Z_p^\times$, and whose residue field is a finite extension of $F_p$. These extensions are used a lot in $p$-adic Hodge theory, so I suggest you look at papers in that area, eg Fontaine's "Arithmétique des représentations galoisiennes $p$-adiques". There's a lot of info about the ramification of that extension, for example. |
Jul 5 |
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Does there exist a non-square number which is the quadratic residue of every prime?
On the other hand, 16 is an 8th power modulo every prime! |
Jul 4 |
comment |
Omitting primes from a Hecke algebra
@Kevin: "So knowing a Galois representation mod 2 does not tell you what the crystalline Frobenius eigenvalues are mod 2". I'm not sure exactly what you mean, but if ell=p, then the mod p Galois repn carries very little information about the Galois repn and the crystalline Frobenius. |
Jun 25 |
awarded | nt.number-theory |