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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 ...
Przemyslaw Chojecki's user avatar
3 votes
0 answers
91 views

Reference request: étale local system on $\Gamma\backslash\mathcal H$ for $\Gamma$ non-congruence

Suppose $\mathcal H$ is the upper half plane, and $\Gamma\subset \operatorname{PSL}_2(\mathbb Z)$ is a finite index subgroup. Then by Belyi's theorem we know that $\Gamma\backslash\mathcal H$ is an ...
Richard's user avatar
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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 ...
user100603's user avatar
2 votes
0 answers
229 views

Reference Request - New proof of Ribet's level lowering by Khare and Wintenberger

I'm currently following the note of Sug Woo Shin's course at Berkeley with notes taken by Rong Zhou. In Section 24.3 (Page 86), Ribet's level lowering theorem is stated: [Theorem 24.7] $E = E_{a^{\...
Hetong Xu's user avatar
  • 639
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 ...
David Corwin's user avatar
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