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arXiv · 1404.5460

Brauer groups on K3 surfaces and arithmetic applications

Kelly McKinnie·Justin Sawon·Sho Tanimoto·Anthony Várilly-Alvarado
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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 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.

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Kelly McKinnie, Justin Sawon, Sho Tanimoto, Anthony Várilly-Alvarado. 2014-04-22. Brauer groups on K3 surfaces and arithmetic applications. https://doi.org/10.1007/978-3-319-46852-5_9

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