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, accounted for by transcendental Brauer-Manin obstructions.
Mathematics Subject Classiffication (2010). 14J28, 14G05, 14F22.
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McKinnie, K., Sawon, J., Tanimoto, S., Várilly-Alvarado, A. (2017). Brauer Groups on K3 Surfaces and Arithmetic Applications. In: Auel, A., Hassett, B., Várilly-Alvarado, A., Viray, B. (eds) Brauer Groups and Obstruction Problems . Progress in Mathematics, vol 320. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-46852-5_9
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DOI: https://doi.org/10.1007/978-3-319-46852-5_9
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-46851-8
Online ISBN: 978-3-319-46852-5
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