Affiliation:
1. Department of Mathematics National University of Singapore Singapore
2. Department of Mathematical Sciences Chalmers University of Technology and the University of Gothenburg Gothenburg Sweden
Abstract
AbstractWe 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, generalizing previous work of Scholze.