Browsing by Author "Frei, Sarah"
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Item Reduction of Brauer classes on K3 surfaces, rationality and derived equivalence(De Gruyter, 2022) Frei, Sarah; Hassett, Brendan; Várilly-Alvarado, AnthonyGiven 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.