Zeta elements for Shimura varieties II: Examples

Abstract: In this second talk, I will begin by reviewing a generalization of the double coset decomposition recipe for parahoric subgroups originally due to Lansky and illustrate the recipe in some simple cases. Paired with the machinery of zeta elements and mixed Hecke correspondences that I described in my previous talk, this decomposition recipe yields a powerful and effective method for studying norm relation problems for classes constructed using the push-forward formalism that would otherwise be too cumbersome to study directly. I will illustrate this method in two key situations of arithmetic interest that were recently studied using alternate methods: Shimura varieties of GU(1,2n-1) & GSp_4. I will also highlight several key technical advantages of this approach over the earlier ones in these cases. Time permitting, I will discuss a new example of an Euler system for the Galois representations arising from GU(2,2) Shimura varieties.

algebraic geometrynumber theory

Audience: researchers in the topic

UCSB Seminar on Geometry and Arithmetic