Perfectoid signature and local étale fundamental group

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.

number theory

Audience: researchers in the topic

( paper )

Comments: pre-talk

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UCSD number theory seminar

Series comments: Most talks are preceded by a pre-talk for graduate students and postdocs. The pre-talks start 40 minutes prior to the posted time (usually at 1:20pm Pacific) and last about 30 minutes.

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