The cohomology of quaternionic Shimura varieties and Ihara’s lemma

Abstract: I will discuss a vanishing theorem for the cohomology of quaternionic Shimura varieties with torsion coefficients, based on a comparison between Igusa varieties inspired by Tian-Xiao's work on the Goren-Oort stratification. I will then explain how to use the theorem, joint with the study of the special fibre at Iwahori level of quaternionic Shimura varieties, in order to prove Ihara's lemma for these varieties. This is joint work (partly in progress) with Ana Caraiani.

algebraic geometrynumber theory

Audience: researchers in the topic

Séminaire de géométrie arithmétique et motivique (Paris Nord)