@inbook{f649d0c5477e49a883686ac8ce0133ee,

title = "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 TS of S; we classify these lattices up to isomorphism using Nikulin{\textquoteright}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.",

keywords = "Brauer groups, K3 surfaces, Projective duality, Special cubic fourfolds, Weak approximation",

author = "Kelly McKinnie and Justin Sawon and Sho Tanimoto and Anthony V{\'a}rilly-Alvarado",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG 2017.",

year = "2017",

doi = "10.1007/978-3-319-46852-5_9",

language = "English",

series = "Progress in Mathematics",

publisher = "Springer Basel",

pages = "177--218",

booktitle = "Progress in Mathematics",

}