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arXiv · 2203.13747

Non-Eisenstein cohomology of locally symmetric spaces for $GL_2$ over a CM field

Shayan Gholami
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Abstract

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.

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Shayan Gholami. 2022-03-25. Non-Eisenstein cohomology of locally symmetric spaces for $GL_2$ over a CM field. https://arxiv.org/abs/2203.13747

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