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arXiv · 2008.00556

On the images of certain $G_2$-valued automorphic Galois representations

Adrian Zenteno
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Abstract

In this paper we study the images of certain families $\{\rho_{\pi,\ell} \}_\ell$ of $G_2$-valued Galois representations of $\mbox{Gal}(\overline{F}/F)$ associated to $L$-algebraic regular, self-dual, cuspidal automorphic representations $\pi$ of $\mbox{GL}_7(\mathbb{A}_F)$, where $F$ is a totally real field. In particular, we prove that, under certain automorphic conditions, the images of the residual representations $\overline{\rho}_{\pi,\ell}$ are as large as possible for infinitely many primes $\ell$. Moreover, we apply our result to some examples constructed by Chenevier, Renard and Ta\"ibi.

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Adrian Zenteno. 2020-08-02. On the images of certain $G_2$-valued automorphic Galois representations. https://arxiv.org/abs/2008.00556

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