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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
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.