Kummer varieties and their brauer groups

Alexei N. Skorobogatov, Yuri G. Zarhin

Research output: Contribution to journalArticle

3 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)337-368
Number of pages32
JournalPure and Applied Mathematics Quarterly
Volume13
Issue number2
DOIs
StatePublished - 2017

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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