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 TS of S; we classify these lattices up to isomorphism using Nikulin’s discriminant form technique. We then study geometric realizations of p-torsion Brauer elements as Brauer-Severi varieties in a few cases via projective duality. We use one of these constructions for an arithmetic application, giving new kinds of counter-examples to weak approximation on K3 surfaces of degree two, accounted for by transcendental Brauer-Manin obstructions.
CITATION STYLE
McKinnie, K., Sawon, J., Tanimoto, S., & Várilly-Alvarado, A. (2017). Brauer groups on K3 surfaces and arithmetic applications. In Progress in Mathematics (Vol. 320, pp. 177–218). Springer Basel. https://doi.org/10.1007/978-3-319-46852-5_9
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