A counterexample to the local-global principle of linear dependence for abelian varieties
Number Theory
2009-05-05 v1
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.
Keywords
Cite
@article{arxiv.0905.0409,
title = {A counterexample to the local-global principle of linear dependence for abelian varieties},
author = {Peter Jossen and Antonella Perucca},
journal= {arXiv preprint arXiv:0905.0409},
year = {2009}
}
Comments
3 pages