Mathematische Annalen

, Volume 348, Issue 4, pp 899–907

A Dirichlet unit theorem for Drinfeld modules

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Abstract

We show that the module of integral points on a Drinfeld module satisfies 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.

Mathematics Subject Classification (2000)

11G09 

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Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Mathematisch InstituutLeidenThe Netherlands

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