论文标题
在某些$ g_2 $可价值的自动形态galois表示形式上
On the images of certain $G_2$-valued automorphic Galois representations
论文作者
论文摘要
在本文中，我们研究了某些家庭的图像$ \ {ρ_{ρ_{ρ_{ρ_{ρ_{p} _ \ ell $的$ g_2 $ -valued galois表示的$ \ mbox {gal}（\ overline {f}/f）$与$ l $ -l $ -l $ -algebraic常规，自selferip $ cuspi utlline {f}/f） $ \ mbox {gl} _7（\ mathbb {a} _f）$，其中$ f $是一个完全真实的字段。特别是，我们证明，在某些自动形态条件下，剩余表示形式的图像$ \overlineρ_{π，\ ell} $对于无限的许多Primes $ \ ell $而言，尽可能大。此外，我们将结果应用于Chenevier，Renard和Taïbi构建的一些例子。
In this paper we study the images of certain families $\{ρ_{π,\ell} \}_\ell$ of $G_2$-valued Galois representations of $\mbox{Gal}(\overline{F}/F)$ associated to $L$-algebraic regular, self-dual, cuspidal automorphic representations $π$ 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 $\overlineρ_{π,\ell}$ are as large as possible for infinitely many primes $\ell$. Moreover, we apply our result to some examples constructed by Chenevier, Renard and Taïbi.
