论文标题
亚代表的单构和低度自动化galois表示的不可约性
Monodromy of subrepresentations and irreducibility of low degree automorphic Galois representations
论文作者
论文摘要
令$ x $为平稳，分开，几何连接的方案，定义在数字字段$ k $和$ \ \ {ρ_λ\}_λ$ n二维半密度$λ$λ$ - adic-adic-adic-aidic of x $ $ x $的系统中$ \ {ρ_{λ，x} \}_λ$是在温和的当地条件下兼容的GALOIS表示系统。对于几乎所有$λ$，我们证明任何类型的不可约束的亚代表$ρ_λ\ otimes \ bar {\ mathbb {q}}} _ \ ell $都是不可记住的。当$ k $完全真实或CM，$ n \ leq 6 $，而$ \ {ρ_λ\}_λ$是$ k $的兼容系统，该系统是$ k $附加到常规代数，偏光，cuspidal cuspidal unormorphic Austromorphic Allothic Allophic Allophic Allmormorphic All for $ \ Mathrm {gl} $ { $λ$我们证明$ρ_λ\ otimes \ bar {\ mathbb {q}}} _ \ ell $ is（i）不可修复，并且（ii）如果另外$ k = \ mathbb {q} $，则（ii）可残留的情况。
Let $X$ be a smooth, separated, geometrically connected scheme defined over a number field $K$ and $\{ρ_λ\}_λ$ a system of n-dimensional semisimple $λ$-adic representations of the étale fundamental group of $X$ such that for each closed point $x$ of $X$, the specialization $\{ρ_{λ,x}\}_λ$ is a compatible system of Galois representations under mild local conditions. For almost all $λ$, we prove that any type A irreducible subrepresentation of $ρ_λ\otimes \bar{\mathbb{Q}}_\ell$ is residually irreducible. When $K$ is totally real or CM, $n\leq 6$, and $\{ρ_λ\}_λ$ is the compatible system of Galois representations of $K$ attached to a regular algebraic, polarized, cuspidal automorphic representation of $\mathrm{GL}_n(\mathbb{A}_K)$, for almost all $λ$ we prove that $ρ_λ\otimes\bar{\mathbb{Q}}_\ell$ is (i) irreducible and (ii) residually irreducible if in addition $K=\mathbb{Q}$.
