Reduction of Purity via Finite Flat Covers and Completion.

Time: 16:00-17:45, 05/03/2026 (Thursday)

Venue: Room 612, A6, Institute of Mathematics-VAST

Online (Join Zoom Meeting) link: https://zoom.us/j/99636681387?pwd=0WscBnehOJig68SqctGluVuA3RwraE.1

 Abstract: In this talk, we explain the reduction steps that allow one to replace the original scheme by a much simpler local model. Following Česnavičius, we show that purity can be tested after passage to suitable finite flat covers and after completion at a closed point. These steps prepare the ground for the perfectoid techniques used later in the proof.

References:

1. [Ga81] O.Gabber, “Some theorems on Azumaya algebras” in The Brauer group (Les Plans-sur-Bex, Switzerland, 1980), Lecture Notes in Math. 844, Springer, Berlin, 1981, 129–209.
2. [Ce19] Česnavičius. Purity for the Brauer group, Duke Mathematical Journal Vol. 168, No. 8, 2019