MIT Number Theory Seminar
Tuesday, October 23, 2018 at 4:30pm to 5:30pm
Jun Su (Princeton)
Title: Automorphy of coherent cohomology of Shimura varieties
Abstract: What are holomorphic/nearly holomorphic automorphic forms in general? The rough anwser is global sections of automorphic vector bundles over Shimura varieties, while to be get things correct for a non-compact Shimura variety one need to take a toroidal compactification of it and consider the canonical extensions of automorphic vector bundles over the compactification. Inspired by Borel and Franke’s work on the cohomology of automophic local systems on locally symmetirc spaces, we prove that the higher cohomology of these extensions can also be computed by automorphic forms, while on the Galois side people (Emerton-Reduzzi-Xiao, Boxer/Goldring-Koskivirta, Pilloni-Stroh) have already attached Galois representations to Hecke eigenclasses in these higher cohomology. In this talk we’ll introduce the relevant constructions, motivate why those cohomology could be interesting, and shed some light on our proof.