Perfectoid Jacquet-Langlands correspondence and the cohomology of Hilbert modular varieties

Abstract: The work of Tian-Xiao on the Goren-Oort stratification for quaternionic Shimura varieties provides a geometric incarnation of the Jacquet-Langlands correspondence, and leads to a geometric approach to level raising of quaternionic automorphic forms. I will describe a perfectoid version of Tian-Xiao's result, and explain how it can be used, joint with geometric properties of the Hodge-Tate period map, to prove vanishing theorems for the cohomology of quaternionic Shimura varieties with torsion coefficients. This is joint work with Ana Caraiani.

algebraic geometrynumber theory

Audience: researchers in the topic

Number Theory Seminars at Università degli Studi di Padova