All Questions
13 questions with no upvoted or accepted answers
16
votes
0
answers
11k
views
Deligne's letter to Jean-Pierre Serre
I'm looking for another letter of Pierre Deligne, this time to Jean-Pierre Serre (from around 1974 I think), in which he proves that the Galois representation associated to a certain Hecke eigenform ...
8
votes
0
answers
335
views
Irreducibility of Galois representations attached to unitary groups
If $G$ is a unitary group in $n$ variables over $\mathbb Q$, attached to an hermitian form for an imaginary quadratic extension $E/\mathbb Q$ and if we suppose that the hermitian form is definite over ...
- 26k
7
votes
0
answers
379
views
Local properties of Galois representations attached to torsion classes
$\DeclareMathOperator{\PGL}{PGL} \DeclareMathOperator{\GL}{GL} \newcommand{\F}{\mathbb{F}} \newcommand{\p}{\mathfrak{p}} \DeclareMathOperator{\Sym}{Sym}$
Let $F$ be a number field, and let $\Gamma$ be ...
- 5,382
5
votes
0
answers
169
views
Where does the notation $\operatorname{Tr}(\cdot)\bmod \ell^\alpha$ implies isomorphism come from?
In J-P Serre's article on Faltings-Serre (Resume du Course 1984-1985) he states (without proof) that for two finite-dimensional $\ell$-adic Galois representations of $\operatorname{Gal}(\mathbb{Q})$, ...
- 2,429
5
votes
0
answers
585
views
Bloch Kato Exponential as formal lie group exponential
Let $K$ be a $p$-adic field and $V$ a $p$-adic representation. In their paper on tamagawa numbers of motives, Bloch and Kato define an exponential map as the connecting homomorphism
$$DR(V) \...
- 3,555
5
votes
0
answers
288
views
Do infinite and ramified local factors of the Dedekind zeta function of a tame number field characterize its local root numbers?
Let say you have two number fields, that are tamely ramified, and suppose that the $p$-part of their Dedekind zeta functions coincide for all prime $p$ which is ramified in either field. Suppose ...
- 2,396
3
votes
0
answers
122
views
Description of $\operatorname{Gal}(K(E[n])/K)$ as a subgroup of $\operatorname{GL}_2(\mathbb{Z}/n\mathbb{Z})$ for a CM elliptic curve $E$
I am looking for a specific description of the Galois groups $\operatorname{Gal}(K(E[n])/K)$ as a subgroup of $\operatorname{GL}_2(\mathbb{Z}/n\mathbb{Z})$ for an elliptic curve $E$ with complex ...
- 309
3
votes
0
answers
152
views
Finiteness of points over the cyclotomic extension for modular forms
Let $\rho(f):G_\mathbb{Q} \rightarrow GL_2(K_f)$ be the Galois representation attached to some cuspidal modular form $f$ where $K_f$ is a finite extension of $\mathbb{Q}_p$.
Let $V_f$ be the vector ...
- 313
2
votes
0
answers
154
views
Categorical representations of absolute Galois groups
I am looking for interesting examples of categorical representations of absolute Galois groups of arithmetic fields. Pointers to the literature would be appreciated.
user127738
1
vote
0
answers
98
views
Are there known effective bounds on the number of semisimple Galois representations?
In continuation to my question here, are there known effective bounds on the total number of semisimple $p$-adic Galois representations unramified outside a finite set of primes $S$, of dimension $d$, ...
- 2,907
1
vote
0
answers
127
views
Multiplicities of Galois representations in the semisimplification of the reduction of a Tate module
Let $C$ be a smooth proper curve, of genus $g$ over a number field $K$. Let $v$ be a prime of good reduction for $C$ above $p>2$, and let $T_pJ$ denote the $p$-adic Tate module of $J$, the Jacobian ...
- 2,907
1
vote
0
answers
131
views
Analytic properties of $L$-functions attached to a compatible system of $\ell$-adic Galois representations
Let $F$ and $E$ be number fields, $G_F$ be the absolute Galois group of $F$, and $S$ be a finite set of primes of $F$. For $\lambda$ a prime of $E$ we denote by $\ell$ its residual characteristic. We ...
- 663
1
vote
0
answers
162
views
Construction of RM abelian variety from eigenform
Let $f$ be a normalized eigenform of weight $2$ level $N$. If the Fourier coefficients of $f$ generate a totally real field $F$, then we associate to $f$ a system of $\ell$-adic Galois representations ...
- 15.4k