Tuesday, January 24, 2023 - 1:45pm
Pretalk title: Brauer groups
Pretalk abstract: I will give a brief discussion of Brauer groups, gerbes, and twisted sheaves.
Main talk title: A geometric Hasse principle for the Brauer group
Main talk abstract: We consider a geometric Hilbertian property for the Brauer group, extending earlier work of Fein, Saltman, Schacher on Brauer-Hilbertian fields. We prove that, for a complex variety S of dimension at least 4 and a Brauer class \alpha \in Br(S), there exist infinitely many codimension 1 points s \in S such that the specialization \alpha|_s \in Br(kappa(s)) has the same period as \alpha. This is joint work with Danny Krashen and Max Lieblich.