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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 |
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$(\varphi, \Gamma)$-modules of finite height
"Since representations that aren't of finite height do exist": take a semistable noncrystalline representation. |
Sep
10 |
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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 |
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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. |