Kummer varieties and their Brauer groups

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Title: Kummer varieties and their Brauer groups
Authors: Skorobogatov, AN
Zarhin, Y
Item Type: Journal Article
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.
Issue Date: 1-Jan-2018
Date of Acceptance: 21-Dec-2017
URI: http://hdl.handle.net/10044/1/57676
DOI: https://dx.doi.org/10.4310/PAMQ.2017.v13.n2.a5
ISSN: 1558-8599
Publisher: International Press
Start Page: 337
End Page: 368
Journal / Book Title: Pure and Applied Mathematics Quarterly
Volume: 13
Issue: 2
Copyright Statement: © 2017 International Press of Boston, Inc. All rights reserved.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/M020266/1
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
ABELIAN-VARIETIES
ELLIPTIC-CURVES
SURFACES
REPRESENTATIONS
PRODUCTS
0101 Pure Mathematics
0102 Applied Mathematics
General Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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