Arithmetic Geometry and Number Theory RTG Seminar: Vanishing theorems for completed cohomology

Seminar | August 27 | 3-5 p.m. | 748 Evans Hall

 David Hansen, University of Notre Dame

 Department of Mathematics

Pre-talk: Completed cohomology, as defined by Calegari and Emerton, is a natural candidate for general spaces of p-adic automorphic forms. I'll give a motivated introduction to completed cohomology and the p-adic Langlands program in the setting of modular curves.

Main talk: I'll discuss some new vanishing theorems for completed cohomology, building on previous work of Scholze and Shen. The proofs involve a fun combination of perfectoid methods and more classical Shimura variety techniques, which I'll try to explain. This is joint work in progress with Christian Johansson.