Christian Johansson: Vanishing theorems for Siegel modular varieties of infinite Gamma_1-level

Abstract: I will discuss a vanishing theorem for singular/etale cohomology with Fp-coefficients as one takes the direct limit over the tower of Siegel modular varieties with Gamma_1(p^n)-level structure. I will focus on the geometry that goes into the proof, and also talk about the motivation and applications of the vanishing theorem, which come from the Langlands programme.

This is joint work in progress with Caraiani, Dotto, Gerbelli-Gauthier, Gulotta, Hsu, Mocz, Reinecke, Santos and Shih.