Brauer groups on K3 surfaces and arithmetic applications
Abstract
For a prime $p$, we study subgroups of order p of the Brauer group Br(S) of a general complex polarized K3 surface of degree 2d, generalizing earlier work of van Geemen. These groups correspond to sublattices of index p of the transcendental lattice T_S of S; we classify these lattices up to isomorphism using Nikulin's discriminant form technique. We then study geometric realizations of ptorsion Brauer elements as BrauerSeveri varieties in a few cases via projective duality. We use one of these constructions for an arithmetic application, giving new kinds of counterexamples to weak approximation on K3 surfaces of degree two.
 Publication:

arXiv eprints
 Pub Date:
 April 2014
 arXiv:
 arXiv:1404.5460
 Bibcode:
 2014arXiv1404.5460M
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Number Theory;
 14J28;
 14G05
 EPrint:
 40 pages