Brauer groups of varieties over local fields of finite characteristic

TL;DR

This paper establishes that the non-log ramification filtration on the Brauer group aligns with the evaluation filtration for schemes over positive characteristic local fields, extending recent results to new settings.

Contribution

It proves the equivalence of two filtrations on the Brauer group in positive characteristic, generalizing prior work from characteristic zero.

Findings

Filtration equivalence for Brauer groups over positive characteristic fields

Extension of existing results to new characteristic settings

Applications to related algebraic geometry problems

Abstract

We show that the non-log version of Kato's ramification filtration on the Brauer group of a separated and finite type regular scheme over a positive characteristic local field coincides with the evaluation filtration. This extends a recent result of Bright-Newton to positive characteristics. Among several applications, we extend some results of Ieronymou, Saito-Sato and Kai to positive characteristics.