2021/11/16 by Sarah Frei, Brendan Hassett, Frei, Sarah +3
Mathematics · #14E08 #14F08 (secondary) #14F22 (primary) #14J28 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2111.08668
openalex publication_date 2021/11/16 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
We consider the reduction of Brauer classes on surfaces over number fields, with a view toward applications to rationality and derived equivalence. We show that a Brauer class on a very general polarized K3 surface over a number field becomes trivial upon reduction for a set of places of positive natural density. As a consequence, there are cubic fourfolds which become rational upon reduction for a positive proportion of places, and there are twisted derived equivalent K3 surfaces which become derived equivalent upon reduction for a positive proportion of places.