Linear dependence in Mordell-Weil groups

DOI10.1515/CRELLE.2009.039zbMath1170.11013arXivmath/0606493MaRDI QIDQ3631302

Krzysztof Górnisiewicz, Wojciech Gajda

Publication date: 5 June 2009

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0606493

zbMATH Keywords

Galois cohomologyabelian varietyKummer theoryMordell-Weil grouplocal-global principle

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10)

Related Items (9)

On a dynamical local-global principle in Mordell-Weil type groups ⋮ A counterexample to the local-global principle of linear dependence for abelian varieties ⋮ On a generalization of the support problem of Erdős and its analogues for abelian varieties and \(K\)-theory ⋮ Commensurability in Mordell-Weil groups of abelian varieties and tori ⋮ On reduction maps and arithmetic dynamics of Mordell–Weil type groups ⋮ Effective results on linear dependence for elliptic curves ⋮ On a reduction map for Drinfeld modules ⋮ On a Hasse principle for Mordell-Weil groups ⋮ Local to global principle for semiabelian varieties isogenous to the product of an abelian variety and a torus

Cites Work

• Finiteness theorems for abelian varieties over number fields.
• Kummer theory on extensions of Abelian varieties by tori
• Detecting linear dependence by reduction maps
• Kummer theory of abelian varieties and reductions of Mordell–Weil groups

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