All Questions
8 questions with no upvoted or accepted answers
6
votes
0
answers
375
views
How to construct this non-geometric mod $p$ Galois representation?
Let $ K $ be a totally real cubic field. I am concerned with the following kind of Inverse Galois Problem:
Is there a prime $ p>5 $ and a continuous representation $ \bar{\rho}:G_{K}\to {\rm
GL}_{...
- 863
4
votes
0
answers
154
views
A variant of the inverse Galois problem
In Theorem I of Construction of maximal unramified p-extensions with prescribed Galois groups, it's proved that
for any prime $p$ and any given finite $p$-group $G$, there exists a number field $F$ ...
- 667
2
votes
0
answers
125
views
Semisimplicity of induced representation of a irreducible representation
This question occurs when I read this one.
Suppose $k$ is a field of char $0$ (not necessarily complex numbers, in my case it's $\mathbb Q_p$), and $G$ is a profinite group (in my case, $\operatorname{...
- 775
2
votes
0
answers
147
views
Prime splitting in the division field of an elliptic curve
Let $E/\mathbb{Q}$ be an elliptic curve with good reduction at two distinct primes $p, \ell$. Suppose the mod $\ell$ Galois representation associated to $E$ is surjective. Let $K=\mathbb{Q}(E[\ell])$ ...
- 1,422
2
votes
0
answers
155
views
Classification of mod p Galois Representations for l not equal to p
Let $l\neq p$ be primes and let $\text{G}_l:=\text{G}_{\mathbb{Q}_l}$. Let $k$ be a finite field of characteristic $p$ and $\bar{\rho}:\text{G}_l\rightarrow \text{GL}_2(k)$ a local Galois ...
user130124
2
votes
0
answers
138
views
Local polynomials of Frobenius-semisimple Weil representations which are tensor products of an Artin representation and an unramified character
Let $K$ be a local field and $\rho: W_K \to \operatorname{GL}(V)$ be a Weil representation. The for any finite extension $F/K$, we define the local polynomial
$$
P(\rho|_F,T) = \det{(1 - \operatorname{...
- 103
1
vote
0
answers
105
views
Local factors determine Weil representations - proof of the Artin representation case
This post can be seen as a continuation of this post I created on MathOverflow.
I want to understand the proof of the following Theorem from "Euler Factors determine Weil Representations" by Tim and ...
- 103
1
vote
0
answers
199
views
Class number of the cyclotomic tower
Let ${\Bbb Q}(\zeta_{\infty})$ be the field obtained by adjoining all roots of unity. We define
Cl(${\Bbb Q}(\zeta_{\infty})$)$\colon= \underset{m > 1}{\varinjlim}~{\mathrm{Cl}}({\Bbb Z}[\zeta_m])...
- 781