The p-primary Brauer group and the perfectoid method.

Time: 14:00-15:45, 06/03/2026 (Friday)

Venue: Room 612, A6, Institute of Mathematics-VAST
Online (Join Zoom Meeting) link: https://zoom.us/j/99636681387?pwd=0WscBnehOJig68SqctGluVuA3RwraE.1

Abstract: The main technical difficulty in purity for the Brauer group lies in controlling the p-
primary torsion. This talk presents the central new input of Česnavičius’s work: a detailed analysis of the p-primary Brauer group in the perfectoid setting. We explain why perfectoid rings naturally arise after the reductions of the first talk, and how almost purity and tilting techniques yield strong vanishing and rigidity results for Brauer groups.

References:

1. [Ce19] Česnavičius. Purity for the Brauer group, Duke Mathematical Journal Vol. 168, No. 8, 2019
2. [KL15] Kedlaya and R. Liu, Relative p-adic Hodge theory: Foundations, Astérisque 371,Soc. Math. France, Paris,2015.