Detecting linear dependence on a semiabelian variety

TL;DR

This paper discusses the conditions under which linear dependence on a semiabelian variety can be detected, highlighting limitations and the need for specific finiteness conditions for the main theorem.

Contribution

It clarifies the validity of the main theorem, showing it only holds under certain finiteness assumptions, and provides counterexamples to previous claims.

Findings

Main theorem is only valid under a finiteness condition.

Counterexamples demonstrate the theorem's limitations.

Clarifies the scope of linear dependence detection.

Abstract

This paper has been withdrawn by the author. The statement of the Main Theorem but is wrong in general, there have been provided counterexamples. The main theorem only holds conditionally, under the finiteness statement of theorem 2.8.