On The Image of Automorphic Galois Representations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913692279373824 |
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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 |
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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 |