$p$-adic hyperbolicity for Shimura varieties and period images

Abstract: Borel proved that every holomorphic map from a product of punctured unit discs to a complex Shimura variety extends to a map from a product of discs to its Bailey-Borel compactification. In joint work with Oswal, Zhu, and Patel, we proved a p-adic version of this theorem over discretely valued fields for Shimura varieties of abelian type. I will speak about work with Bakker, Oswal, and Yao, where we prove the analogous $p$-adic extension theorem for compact non-abelian Shimura varieties and geometric period images for large primes $p$.

number theory

Audience: researchers in the topic

BC-MIT number theory seminar