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arXiv · 0905.0409

A counterexample to the local-global principle of linear dependence for abelian varieties

Peter Jossen·Antonella Perucca
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Abstract

Let A be an abelian variety defined over a number field k. Let P be a point in A(k) and let X be a subgroup of A(k). Gajda in 2002 asked whether it is true that the point P belongs to X if and only if the point (P mod p) belongs to (X mod p) for all but finitely many primes p of k. We answer negatively to Gajda's question.

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Peter Jossen, Antonella Perucca. 2009-05-04. A counterexample to the local-global principle of linear dependence for abelian varieties. https://arxiv.org/abs/0905.0409

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