researchseminars.org

Hanlin Cai (Utah)
2023-05-04 21:00 - 22:00 UTC | https://researchseminars.org/talk/UCSD_NTS/91/
Title: Perfectoid signature and local étale fundamental group (https://researchseminars.org/talk/UCSD_NTS/91/)
by Hanlin Cai (Utah) as part of UCSD number theory seminar

Lecture held in APM 6402 and online.

Abstract
In this talk I'll talk about a (perfectoid) mixed characteristic version of F-signature and Hilbert-Kunz multiplicity by utilizing the perfectoidization functor of Bhatt-Scholze and Faltings' normalized length. These definitions coincide with the classical theory in equal characteristic. Moreover, perfectoid signature detects BCM regularity and transforms similarly to F-signature or normalized volume under quasi-étale maps. As a consequence, we can prove that BCM-regular rings have finite local étale fundamental group and torsion part of their divisor class groups. This is joint work with Seungsu Lee, Linquan Ma, Karl Schwede and Kevin Tucker.

pre-talk
