Hasse principle for Kummer varieties
File(s)
Accepted version
Author(s)
Harpaz, Y
Skorobogatov, AN
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.
Date Issued
2016-06-20
Date Acceptance
2016-03-12
Citation
Algebra and Number Theory, 2016, 10 (4), pp.813-841
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
Engineering & Physical Science Research Council (EPSRC)
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000384735800005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Grant Number
EP/M020266/1
Subjects
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