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arXiv · 2011.03951

Perfectoid Shimura varieties and the Calegari-Emerton conjectures

David Hansen·Christian Johansson
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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.

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David Hansen, Christian Johansson. 2020-11-08. Perfectoid Shimura varieties and the Calegari-Emerton conjectures. https://arxiv.org/abs/2011.03951

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