Frei, SarahHassett, BrendanVárilly-Alvarado, Anthony2022-12-132022-12-132022Frei, Sarah, Hassett, Brendan and Várilly-Alvarado, Anthony. "Reduction of Brauer classes on K3 surfaces, rationality and derived equivalence." <i>Journal für die reine und angewandte Mathematik,</i> 2022, no. 792 (2022) De Gruyter: 289-305. https://doi.org/10.1515/crelle-2022-0056.https://hdl.handle.net/1911/114136Given a smooth projective variety over a number field and an element of its Brauer group, we consider the specialization of the Brauer class at a place of good reduction for the variety and the class. We are interested in the case of K3 surfaces. We show that a Brauer class on a very general polarized K3 surface over a number field becomes trivial after specialization at a set of places of positive natural density. We deduce that there exist cubic fourfolds over number fields that are conjecturally irrational, with rational reduction at a positive proportion of places. We also deduce that there are twisted derived equivalent K3 surfaces which become derived equivalent after reduction at a positive proportion of places.engThis is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by De Gruyter.Journal articlehttps://doi.org/10.1515/crelle-2022-0056