4,607 reputation
11533
bio website perso.ens-lyon.fr/…
location Lyon, France
age 37
visits member for 3 years, 11 months
seen yesterday
I am a number theorist working in Lyon (France).

Feb
6
comment Status of local Langlands conjecture over positive characteristic
Laumon pas Laumont!
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
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 :)
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
comment 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
24
comment Is there a known example of a curve X of genus > 1 over Q such that we know the number of points of X over the n-th cyclotomic field, for every n?
Concerning solvable points on projective curves: there are some results of Ciperiani and Wiles "Solvable points on genus one curves" and of Pal as well "Solvable points on projective algebraic curves", "Solvable points on genus one curves over local fields" and "Curves which do not become semi-stable after any solvable extension".
Jun
7
comment Roadmap to reach Arithmetic Geometry for a Physics Major
Take a look at the book "From Number Theory to Physics". Exerpt from the blurb : "The 14 chapters of this book are extended, self-contained versions of expository lecture courses given at a school on "Number Theory and Physics" held at Les Houches for mathematicians and physicists. Most go as far as recent developments in the field. Some adapt an original pedagogical viewpoint."
Apr
4
comment A criterion for freeness over a local ring
Great, thank you!
Dec
17
comment Commuting invariants and duals of C_p vector spaces
Concerning your first question: a $G_K$-equivariant map from V to $C_p$ exists, for example, whenever $V$ is of Hodge-Tate type with one weight equal to $0$. This happens for lots of repns for which $V^{G_K} = 0$.
Dec
4
comment Algebraic maximal extension and algebraic closure
$\mathbf{C}_p$ has plenty of immediate extensions, that is extensions that have the same value group and the same residue field. The compositum of all these is its spherical completion. Now lots of intermediate fields between $\mathbf{C}_p$ and its spherical completion would not be algebraic maximal.
Nov
23
comment I know that you know…
There is a (not serious) mention of this in "A canticle for Leibowitz", but sadly I don't remember where exactly. Can somebody find the exact quotation?
Nov
17
comment Why is Gauss credited with his connection?
Ah, so the story about Gauss inventing the least squares method to compute orbital parameters of asteroids is bogus?
Nov
16
comment Absolute Galois group of the field of Puiseux series over $\overline{\mathbb{F}}_p$
@Spice: if you replace $\overline{\mathbb{F}}_p$ iwth $\mathbb{C}$, then the field you get is algebraically closed.
Oct
24
comment Slick ways to make annoying verifications
@Charles : yes, sorry, I forgot to say "free", so the modules should be free of the same rank. Thanks.