A Dirichlet unit theorem for Drinfeld modules

TL;DR

This paper establishes a Dirichlet unit theorem analogue for Drinfeld modules, providing a canonical finitely generated sub-module of integral points and formulating a conjectural class number formula.

Contribution

It introduces a Dirichlet unit theorem analogue for Drinfeld modules and constructs a canonical finitely generated sub-module of integral points.

Findings

Module of integral points satisfies Dirichlet's unit theorem analogue

Constructs a canonical finitely generated sub-module

Formulates a conjectural class number formula

Abstract

We show that the module of integral points on a Drinfeld module satisfies a an analogue of Dirichlet's unit theorem, despite its failure to be finitely generated. As a consequence, we obtain a construction of a canonical finitely generated sub-module of the module of integral points. We use the results to give a precise formulation of a conjectural analogue of the class number formula.