Reduction of Brauer classes on K3 surfaces, rationality and derived equivalence
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2021
- DOI:
- 10.48550/arXiv.2111.08668
- arXiv:
- arXiv:2111.08668
- Bibcode:
- 2021arXiv211108668F
- Keywords:
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- Mathematics - Algebraic Geometry;
- Mathematics - Number Theory;
- 14J28;
- 14F22 (primary);
- 14E08;
- 14F08 (secondary)
- E-Print:
- 23 pages