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Article Dans Une Revue Algebra & Number Theory Année : 2016

Hasse principle for Kummer varieties

Résumé

The existence of rational points on Kummer varieties associated to 2-coverings of abelian varieties over number fields can sometimes be proved through the variation of the Selmer group in the family of quadratic twists of the underlying abelian variety, using an idea of Swinnerton-Dyer. Following Mazur and Rubin, we consider the case when the Galois action on the 2-torsion has a large image. Under mild additional hypotheses we prove the Hasse principle for the associated Kummer varieties assuming the finiteness of relevant Shafarevich-Tate groups.

Dates et versions

hal-02409223 , version 1 (13-12-2019)

Identifiants

Citer

Yonatan Harpaz, Alexei N. Skorobogatov. Hasse principle for Kummer varieties. Algebra & Number Theory, 2016, 10 (4), pp.813-841. ⟨10.2140/ant.2016.10.813⟩. ⟨hal-02409223⟩
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