Vanishing theorems for the cohomology of Shimura varieties

Abstract: I will survey some vanishing theorems for the mod $p$ cohomology of Shimura varieties. I will mention some $p$-adic results and some $\ell$-adic results, where $\ell$ is a prime different from $p$. Both settings rely on the geometry of the Hodge-Tate period morphism. I will highlight the differently flavoured techniques that are needed using the toy model of the modular curve. I will end by discussing joint work in progress with Matteo Tamiozzo in the case of Hilbert modular varieties.

number theoryrepresentation theory

Audience: researchers in the topic

Cross Atlantic Representation Theory and Other topics ONline (CARTOON) conference