On The Image of Automorphic Galois Representations

Fuente: arXiv
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Main Author: Shavali, Alireza
Format: Preprint
Published: 2025
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author Shavali, Alireza
author_facet Shavali, Alireza
contents In this paper, we study extra-twists for automorphic representations of $\mathrm{GL}_n$ and use them to give a precise description of the image of the Galois representations associated with regular algebraic cuspidal automorphic representations of $\mathrm{GL}_3$ over totally real fields. We also formulate a conjecture for the $\mathrm{GL}_n$-case and show how it follows from some standard conjectures in the Langlands program. Finally, assuming the existence of a motive associated with the representation, we study the relation of our constructions with the Mumford-Tate group.
format Preprint
id arxiv_https___arxiv_org_abs_2502_10799
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On The Image of Automorphic Galois Representations
Shavali, Alireza
Number Theory
11F80
In this paper, we study extra-twists for automorphic representations of $\mathrm{GL}_n$ and use them to give a precise description of the image of the Galois representations associated with regular algebraic cuspidal automorphic representations of $\mathrm{GL}_3$ over totally real fields. We also formulate a conjecture for the $\mathrm{GL}_n$-case and show how it follows from some standard conjectures in the Langlands program. Finally, assuming the existence of a motive associated with the representation, we study the relation of our constructions with the Mumford-Tate group.
title On The Image of Automorphic Galois Representations
topic Number Theory
11F80
url https://arxiv.org/abs/2502.10799