Detecting linear dependence on a simple abelian variety

Abstract

Let A be a geometrically simple abelian variety over a number field k, let X be a subgroup of A(k) and let P be an element of A(k). We prove that if P belongs to X modulo almost all primes of k then P already belongs to X.

arXiv comment24 pages

References in corpus (2)

• Kummer theory of abelian varieties and reductions of Mordell-Weil groups
• On the problem of detecting linear dependence for products of abelian varieties and tori

Cited by in corpus (1)

• On the Mumford-Tate conjecture for 1-motives