Sarah Frei, April 22, 2022

Title: Reduction of Brauer classes on K3 surfaces

Abstract: For a very general polarized K3 surface over the rational numbers, it is a consequence of the Tate conjecture that the Picard rank jumps upon reduction modulo any prime. This jumping in the Picard rank is countered by a drop in the size of the Brauer group. In this talk, I will report on joint work with Brendan Hassett and Anthony Várilly-Alvarado, in which we consider the following: Given a non-trivial Brauer class on a very general polarized K3 surface over Q, how often does this class become trivial upon reduction modulo various primes? This has implications for the rationality of reductions of cubic fourfolds as well as reductions of twisted derived equivalent K3 surfaces.