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Hasse principle for Kummer varieties

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Title: Hasse principle for Kummer varieties
Authors: Harpaz, Y
Skorobogatov, AN
Item Type: Journal Article
Abstract: The existence of rational points on the Kummer variety associated to a 22-covering of an abelian variety AA over a number field can sometimes be established through the variation of the 22-Selmer group of quadratic twists of AA. In the case when the Galois action on the 22-torsion of AA has a large image, we prove, under mild additional hypotheses and assuming the finiteness of relevant Shafarevich–Tate groups, that the Hasse principle holds for the associated Kummer varieties. This provides further evidence for the conjecture that the Brauer–Manin obstruction controls rational points on K3 surfaces.
Issue Date: 20-Jun-2016
Date of Acceptance: 12-Mar-2016
URI: http://hdl.handle.net/10044/1/42590
DOI: https://dx.doi.org/10.2140/ant.2016.10.813
ISSN: 1944-7833
Publisher: Mathematical Sciences Publishers (MSP)
Start Page: 813
End Page: 841
Journal / Book Title: Algebra and Number Theory
Volume: 10
Issue: 4
Copyright Statement: © 2016 Mathematical Sciences Publishers
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/M020266/1
Keywords: Science & Technology
Physical Sciences
Mathematics
Kummer varieties
Hasse principle
ABELIAN-VARIETIES
ELLIPTIC-CURVES
RATIONAL-POINTS
BRAUER GROUP
SURFACES
RANKS
THEOREM
TWISTS
General Mathematics
0101 Pure Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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