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.
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