On a Hasse principle for Mordell-Weil groups

TL;DR

This paper proves a Hasse principle for determining linear dependence of non-torsion points in the Mordell-Weil group of abelian varieties over number fields, linking local and global properties.

Contribution

It establishes a new Hasse principle that connects local linear dependence conditions to global linear dependence in Mordell-Weil groups.

Findings

Proves a Hasse principle for Mordell-Weil groups over number fields.

Links local linear dependence to global linear dependence.

Advances understanding of rational points on abelian varieties.

Abstract

In this paper we establish a Hasse principle concerning the linear dependence over $\Z$ of nontorsion points in the Mordell-Weil group of an abelian variety over a number field.