Vanishing of Brauer classes on K3 surfaces under reduction

Number Theory
Wednesday, November 1, 2023 - 3:30pm for 1 hour (actually 50 minutes)
Skiles 006
Salim Tayou – Harvard University – tayou@math.harvard.edu
Alex Dunn

Given a Brauer class on a K3 surface over a number field, we prove that there exists infinitely many primes where the reduction of the Brauer class vanishes, under some mild assumptions. This answers a question of Frei--Hassett--Várilly-Alvarado. The proof uses Arakelov intersection theory on GSpin Shimura varieties. If time permits, I will explain some applications to rationality questions. The results in this talk are joint work with Davesh Maulik.