Automorphy and irreducibility of some l-adic representations
Automorphy and irreducibility of some l-adic representations
复制标题
一些 l-adic 表示的自同构和不可约性
DOI：
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发表时间：
2013
影响因子：
1.8
通讯作者：
Richard Taylor
中科院分区：
文献类型：
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作者：
Stefan Patrikis;Richard Taylor
本文证明了一个纯的、正则的、全奇的、可极化的弱相容$L表示系统是蕴含自同构的。创新之处在于，我们没有做不可约性假设，而是做了一个纯粹的假设。对于来自几何学的兼容系统，纯度通常比不可约性更容易检查。我们使用Katz的刚性局部系统理论来构造我们的定理适用的许多动机的例子。我们还证明了：如果$F$是CM域或全实域，且${itpi}$是$ext{GL}_{n}(mathbb{A}_{F})$的可极化正则代数自同构表示，则对于有理素数$L$的正狄里克莱特密度集，与${itpi}$相关的$L$-ady表示$r_{L，imath}({itpi})$是不可约的。
Abstract In this paper we prove that a pure, regular, totally odd, polarizable weakly compatible system of $l$-adic representations is potentially automorphic. The innovation is that we make no irreducibility assumption, but we make a purity assumption instead. For compatible systems coming from geometry, purity is often easier to check than irreducibility. We use Katz’s theory of rigid local systems to construct many examples of motives to which our theorem applies. We also show that if $F$ is a CM or totally real field and if ${itpi}$ is a polarizable, regular algebraic, cuspidal automorphic representation of $ ext{GL}_{n}(mathbb{A}_{F})$, then for a positive Dirichlet density set of rational primes $l$, the $l$-adic representations $r_{l,imath }({itpi})$ associated to ${itpi}$ are irreducible.