All Questions
Tagged with galois-representations rt.representation-theory
64 questions
7
votes
1
answer
914
views
Explicit calculation of Weil Deligne representations
According to Grothendieck monodromy theorem, l-adic galois representations of a local field corresponds to Weil-Deligne representations.
However, given a galois representation, it is usually difficult ...
- 945
6
votes
2
answers
985
views
Irreducible representations of compact groups
Let G be a compact group (or even profinite - Galois group). Let $V$ be a vector space over the field ${\mathbb F}_p$ with $p$ elements, $p$ a finite prime, such that $V$ is a contable product of ${\...
- 63.9k
4
votes
1
answer
202
views
Pro-$l$ Sylow action in a primitive representation of inertia over $\overline{\mathbb{F}}_l$
Let $K$ be a nonarchimedean local field of residue characteristic $p \neq l$ and let $I_K$ be the inertia subgroup of its absolute Galois group. Let $V$ an irreducible representation of $I_K$ over $\...
- 5,363
7
votes
0
answers
570
views
Which de Rham representations are trianguline?
Let $K/\mathbf{Q}_p$ be a finite extension, and let $V$ be an $n$-dimensional $\overline{\mathbf{Q}_p}$-vector space with a continuous action of $G_K$. Suppose $V$ is de Rham, so potentially ...
- 13.1k
3
votes
0
answers
199
views
Decompositions of representations of pro-p groups
Let $P$ be a pro-p group. Assume that there is a filtration of $P$ by normal subgroups $P_i$ such that $P_0=P$ and $P_{i+1} < P_i(i\in\mathbb N)$. Let $V$ be an $l$-adic representation of $P$, ...
- 93
23
votes
3
answers
4k
views
Subgroups of GL(2,q)
I have been wondering about something for a while now, and the simplest incarnation of it is the following question:
Find a finite group that is not a subgroup of any $GL_2(q)$.
Here, $GL_2(q)$ is ...
- 1,169
31
votes
1
answer
5k
views
Modern proof of Serre's open image theorem?
Let $E$ be an elliptic curve defined over a number field $K$ without complex multiplication. Serre's open image theorem (which appears in his book 'Abelian $l$-Adic Representations and Elliptic Curves'...
- 1,905
3
votes
0
answers
740
views
The operator \boxtimes and \boxplus in automorphic representations
Given two automorphic representations $\pi_1, \pi_2$ of $GL_2(\mathbb A_Q)$ and $GL_3(\mathbb A_Q)$ respectively. Let $\pi_i =\otimes_v \pi_{i, v}$.
Now, for each $v$, let $\pi_{1, v}\boxtimes \pi_{...
- 31
14
votes
2
answers
2k
views
"Purely local" proof of local Langlands
As from this website
http://math.uchicago.edu/~lxiao/workshop_site/
My question is: What does it mean by "purely local"?
Also, I heard about this phrase "purely local" in other problems as well, ...
- 4,487
2
votes
1
answer
449
views
$l$-adic representations from Shimura curves
This question may be kind of vague. And we use the same notations as in Carayol's papers:
H. Carayol, Sur les représentations l-adiques associées aux formes modulaires de Hilbert;
H. Carayol, Sur la ...
- 37k
1
vote
1
answer
274
views
Dimension of fixed points of Galois group actions
I have a question about fixed points of Galois group actions.
I am hoping that this is easy for the experts.
Let $k$ be a field of characteristic $0$. Let $K$ be a finite
Galois extension of $k$ ...
- 866
4
votes
0
answers
380
views
Which properties of p-adic representations can be recovered from (\varphi,\Gamma)-modules?
In Berger's "An introduction to the Theory of $p$-adic Representations", he mentions that due the the equivalence of categories between etale $(\varphi,\Gamma)$-modules and $p$-adic representations, ...
- 41
4
votes
2
answers
1k
views
Galois theory of endomorphism rings of irreducible representations
Let $k$ be a field which I don't suppose to be algebraically closed. Then, the endomorphism ring of any irreducible representation of a finite group over $k$ is a division ring.
What is known about ...
- 3,246
8
votes
2
answers
1k
views
number of irreducible representations over general fields
For a finite group, there are finitely many irreducible representations of complex numbers.
What if the field is changed to some other fields? Like real numbers, p-adic field, finite field?
In ...
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