Locally analytic completed cohomology
Number Theory
2026-04-10 v4
Abstract
We compute the geometric Sen operator for arbitrary Shimura varieties in terms of equivariant vector bundles of flag varieties and the Hodge-Tate period map. As an application, we obtain the rational vanishing of completed cohomology in the Calegari-Emerton conjectures.
Keywords
Cite
@article{arxiv.2209.01057,
title = {Locally analytic completed cohomology},
author = {J. E. Rodríguez Camargo},
journal= {arXiv preprint arXiv:2209.01057},
year = {2026}
}
Comments
Accepted version. To appear in JAMS