论文标题
关于以开放图像的还原组价值的Galois表示形式的注释
A note on Galois representations valued in reductive groups with open image
论文作者
论文摘要
令$ g $为$ \ dim z（g）\ leq 1 $的分裂还原组。我们表明，对于任何相对于$ g $的prime $ p $，都有一个有限的分支galois表示形式$ρ\colonγ_{\ mathbb q} \ to g（\ mathbb z_p）$带有开放图像。我们还表明，对于任何给定的整数$ e $，如果$ p $的不规则索引最多是$ e $，并且如果$ p $相对于$ g $和$ g $和$ e $足够大，那么就有一个galois表示$γ_{\ mathbb q} \ to g（\ mathbb z_p z_p z_p）$ ram prom per per per a a。通过将合适的Galois表示形式提升到$ g（\ Mathbb f_p）$中，使用Fakhruddin-khare-khare-patrikis升级为$ g（\ mathbb f_p）$来构建第一种类型的Galois表示形式，第二种类型的Galois表示形式是使用Ray参数的变体构建的。
Let $G$ be a split reductive group with $\dim Z(G) \leq 1$. We show that for any prime $p$ that is large enough relative to $G$, there is a finitely ramified Galois representation $ρ\colon Γ_{\mathbb Q} \to G(\mathbb Z_p)$ with open image. We also show that for any given integer $e$, if the index of irregularity of $p$ is at most $e$ and if $p$ is large enough relative to $G$ and $e$, then there is a Galois representation $Γ_{\mathbb Q} \to G(\mathbb Z_p)$ ramified only at $p$ with open image, generalizing a theorem of A. Ray. The first type of Galois representation is constructed by lifting a suitable Galois representation into $G(\mathbb F_p)$ using a lifting theorem of Fakhruddin--Khare--Patrikis, and the second type of Galois representation is constructed using a variant of Ray's argument.
