Number Theory Seminar

In this talk, I will describe joint work with Peter Scholze on the geometry of the Hodge-Tate period morphism for perfectoid Shimura varieties. This relies on an infinite-level version of the Mantovan product formula that relates Rapoport-Zink spaces, Igusa varieties, and Shimura varieties. I will explain how to extend this result to the boundary of minimal and toroidal compactifications and mention applications to the cohomology of Shimura varieties and beyond.