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2016 Hasse principle for Kummer varieties
Yonatan Harpaz, Alexei Skorobogatov
Algebra Number Theory 10(4): 813-841 (2016). DOI: 10.2140/ant.2016.10.813

Abstract

The existence of rational points on the Kummer variety associated to a 2-covering of an abelian variety A over a number field can sometimes be established through the variation of the 2-Selmer group of quadratic twists of A. In the case when the Galois action on the 2-torsion of A 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.

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Yonatan Harpaz. Alexei Skorobogatov. "Hasse principle for Kummer varieties." Algebra Number Theory 10 (4) 813 - 841, 2016. https://doi.org/10.2140/ant.2016.10.813

Information

Received: 8 May 2015; Revised: 8 February 2016; Accepted: 12 March 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1369.14032
MathSciNet: MR3519097
Digital Object Identifier: 10.2140/ant.2016.10.813

Subjects:
Primary: 14G05
Secondary: 11J95

Rights: Copyright © 2016 Mathematical Sciences Publishers

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Vol.10 • No. 4 • 2016
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