Perfectoid towers and global purity

Time: 16:00-17:45, 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: This talk explains how the local results obtained via perfectoid methods lead to a full
proof of purity for the Brauer group of regular schemes. After the reductions and the analysis of the p-primary Brauer group in the perfectoid case, the remaining task is to descend Brauer classes along infinite perfect or perfectoid towers. That is the content of Lemma 5.1 and 5.2 in [Ce19] where one can “embed” a given regular local ring into a filtered colimit of finite flat extensions whose limit is perfectoid. After that, by using the local-global argument, we deduce the Global purity.

Reference:

1. [Ce19] Česnavičius. Purity for the Brauer group, Duke Mathematical Journal Vol.168, No. 8, 2019