@article{eed731aa2d654933b990ee75b4d16443,
title = "Kummer varieties and their brauer groups",
abstract = "We study Kummer varieties attached to 2-coverings of abelian varieties of arbitrary dimension. Over a number field we show that the subgroup of odd order elements of the Brauer group does not obstruct the Hasse principle. Sufficient conditions for the triviality of the Brauer group are given, which allow us to give an example of a Kummer K3 surface of geometric Picard rank 17 over the rationals with trivial Brauer group. We establish the non-emptyness of the Brauer–Manin set of everywhere locally soluble Kummer varieties attached to 2-coverings of products of hyperelliptic Jacobians with large Galois action on 2-torsion.",
author = "Skorobogatov, {Alexei N.} and Zarhin, {Yuri G.}",
note = "Funding Information: The first named author was partially supported by a grant EP/M020266/1 from EPSRC. The work on this paper started when he was visiting the Pennsylvania State University and continued when he was at the Institute for Advanced Study in Princeton, where he was supported by The Charles Simonyi Endowment. He is grateful to both institutions. The second named author was partially supported by a grant from the Simons Foundation (grant 246625 to Yuri Zarkhin). A part of this work was done while he was a visitor at the Max-Planck-Institut f{\"u}r Mathematik in Bonn, whose hospitality and support are gratefully acknowledged. We would like to thank Yonatan Harpaz for extremely helpful comments and Samir Siksek for directing us to the paper [3]. We are grateful to Tatiana Bandman and the referees for their comments. Publisher Copyright: {\textcopyright} 2017, International Press of Boston, Inc. All rights reserved.",
year = "2017",
doi = "10.4310/PAMQ.2017.v13.n2.a5",
language = "English (US)",
volume = "13",
pages = "337--368",
journal = "Pure and Applied Mathematics Quarterly",
issn = "1558-8599",
publisher = "International Press of Boston, Inc.",
number = "2",
}