On exotic Hecke correspondences | BIMSA-YMSC Tsinghua Number Theory Seminar

Abstract

The goal of this talk is to explain joint work in progress with Jack Sempliner on the construction of "exotic" Hecke correspondences between the mod p fibers of different Shimura varieties of Hodge type. Our work generalizes forthcoming work of Xiao-Zhu; our results cover the new situation where the groups underlying the two different Shimura varieties are allowed to be to be non-isomorphic at p. As a consequence of our main results, we obtain exotic isomorphisms of Igusa varieties in the style of Caraiani-Tamiozzo which lead to geometric incarnations of the Jacquet--Langlands correspondence.