# A variant of Siegel's theorem for Drinfeld modules

## TL;DR

This paper extends Siegel's theorem to finitely generated submodules under Drinfeld module action, providing a significant advancement in understanding the arithmetic of Drinfeld modules.

## Contribution

It completes the proof of a Siegel type statement for finitely generated submodules of the additive group under Drinfeld module action.

## Key findings

- Established a Siegel type finiteness result for Drinfeld modules
- Extended classical Diophantine finiteness theorems to function field setting
- Provided new tools for studying arithmetic properties of Drinfeld modules

## Abstract

We complete the proof of a Siegel type statement for finitely generated $\Phi$-submodules of $\mathbb{G}_a$ under the action of a Drinfeld module $\Phi$.