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

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

2009-05-04

arxiv.org/abs/0905.0409v1

Mathematics

Number Theory

3 pages

Scientific paper

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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