Automorphy for coherent cohomology of Shimura varieties

Joint IAS/Princeton University Number Theory Seminar
Topic:Automorphy for coherent cohomology of Shimura varieties
Speaker:Jun Su
Affiliation:Princeton University
Date:Tuesday, December 5
Time/Room:4:45pm - 5:45pm/S-101
Video Link:https://video.ias.edu/puias/2017/1205-JunSu

We consider the coherent cohomology of toroidal compactifications of Shimura varieties with coefficients in the canonical extensions of automorphic vector bundles and show that they can be computed as relative Lie algebra cohomology of automorphic representations. Consequently, any Galois representation attached to these coherent cohomology should be automorphic. Our proof is based on Franke’s work on singular cohomology of locally symmteric spaces and via Faltings’ B-G-G spectral sequence we’ve also strengthened Franke’s result in the Shimura variety case.