Back to Commutative Algebra Seminar: Fall 2024
Commutative Algebra Seminar
Date: Friday, Dec 6, 2024
Time: 2:00PM - 3:00PM
Location: LCB 222
Joint with RT/NT
Tongmu He
Princeton University
Title |
Perfectoidness via Sen Theory and Applications to Shimura Varieties |
Abstract |
There is a longstanding question about the perfectoidness of Shimura varieties at infinite level, which would lead to a profound connection between étale cohomology and coherent cohomology. In this talk, we will develop a p-adic Hodge theory for general valuation rings, generalizing Tate’s work on discrete valuation rings. This enables us to establish “stalkwise perfectoidness” for Shimura varieties at infinite level, which is sufficient for such a connection. As an application, we prove that the integral completed cohomology groups vanish in higher degrees, verifying a conjecture of Calegari-Emerton for arbitrary Shimura varieties. This is my recent work arXiv.2407.14488. |
Commutative Algebra