Vanishing of non-Eisenstein cohomology of locally symmetric spaces for $\mathrm{GL}_2$ over a CM field

Abstract: Locally symmetric spaces are generalizations of modular curves, and their cohomology plays an important role in the Langlands program. In this talk, I will first speak about vanishing conjectures and known results about the cohomology of locally symmetric spaces of a reductive group $G$ with mod $p$ coefficient after localizing at a maximal ideal of spherical Hecke algebra of $G$ and after that, I will explain a sketch of my proof for the case $G = \mathrm{GL}_2(F)$, where $F$ is a CM field.

algebraic geometrynumber theory

Audience: researchers in the topic

Séminaire de géométrie arithmétique et motivique (Paris Nord)