Vanishing of Brauer classes on K3 surfaces under reduction

Abstract

Given a Brauer class on a K3 surface defined over a number field, we prove that there exists infinitely many reductions where the Brauer class vanishes, under certain technical hypotheses, answering a question of Frei--Hassett--Várilly-Alvarado.

Fixed an erroneous Lemma and some other minor typos. Main result unchanged. Added a corollary about applications to elliptic fibrations on K3 surfaces. To appear in the Journal of the London Mathematical Society