The Mordell-Lang Theorem for Drinfeld modules

TL;DR

This paper proves a Mordell-Lang theorem for Drinfeld modules in both finite and generic characteristic cases, advancing the understanding of their algebraic and definable structures.

Contribution

It establishes the Mordell-Lang theorem for Drinfeld modules of finite and generic characteristic, using quasi-endomorphism rings and specialization techniques.

Findings

Proved Mordell-Lang theorem for finite characteristic Drinfeld modules

Extended the theorem to generic characteristic using specialization

Analyzed the quasi-endomorphism ring of definable subgroups

Abstract

We study the quasi-endomorphism ring of infinitely definable subgroups in separably closed fields. Based on the results we obtain, we are able to prove a Mordell-Lang theorem for Drinfeld modules of finite characteristic. Using specialization arguments we are able to prove also a Mordell-Lang theorem for Drinfeld modules of generic characteristic.