On arithmetic in Mordell-Weil groups

TL;DR

This paper explores how to detect linear dependence among points in Mordell-Weil groups of abelian varieties using reduction maps, aiming to establish conditions for effective detection through finite reductions.

Contribution

It provides new criteria for identifying linear dependence in Mordell-Weil groups based on reduction maps, enhancing understanding of their structure.

Findings

Established conditions for detecting linear dependence via reductions

Identified limitations and capabilities of reduction maps in Mordell-Weil groups

Improved methods for analyzing abelian varieties' rational points

Abstract

In this paper we investigate linear dependence of points in Mordell-Weil groups of abelian varieties via reduction maps. In particular we try to determine the conditions for detecting linear dependence in Mordell-Weil groups via finite number of reductions.