Perfectoid Shimura varieties and the Calegari-Emerton conjectures
Number Theory
2025-09-01 v2 Algebraic Geometry
Representation Theory
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.
Keywords
Cite
@article{arxiv.2011.03951,
title = {Perfectoid Shimura varieties and the Calegari-Emerton conjectures},
author = {David Hansen and Christian Johansson},
journal= {arXiv preprint arXiv:2011.03951},
year = {2025}
}
Comments
Accepted version