Perfectoid Shimura varieties and the Calegari-Emerton conjectures
David Hansen, Christian Johansson
公開日: 2020/11/8
Abstract
We prove many new cases of a conjecture of Calegari-Emerton describing the qualitative properties of completed cohomology. The heart of our argument is a careful inductive analysis of completed cohomology on the Borel-Serre boundary. As a key input to this induction, we prove a new perfectoidness result for towers of minimally compactified Shimura varieties of pre-abelian type, generalizing previous work of Scholze.