论文标题
$ gl_2 $在CM字段上的本地对称空间的非Eisenstein共同学
Non-Eisenstein cohomology of locally symmetric spaces for $GL_2$ over a CM field
论文作者
论文摘要
令$ f $为CM字段，让$ p $为素数。本文的目的是在温和条件下表明，本地对称空间的模式$ p $同时$ x $ $ gl_2（f）$ for prime to prime to $ p $属于Borel-Wallach范围$ [q_0，Q_0，Q_0，Q_0+\ ell_0] $在本地化的he ece nonnonnonnonly-nor-saxean heec eSENSEAL之后。从这个结果，我们将预期的后果推断为对第一个和最后的共同体学组的结构，作为Hecke代数的模块。
Let $F$ be a CM field, let $p$ be a prime number. The goal of this paper is to show, under mild conditions, that the modulo $p$ cohomology of the locally symmetric spaces $X$ for $GL_2(F)$ with level prime to $p$ is concentrated in degrees belonging to the Borel-Wallach range $[q_0,q_0+\ell_0]$ after localizing at a "strongly non-Eisenstein" maximal ideal of the Hecke algebra. From this result, we deduce expected consequences on the structure of the first and last cohomology groups as modules over the Hecke algebra.
