A Dirichlet unit theorem for Drinfeld modules
Number Theory
2010-08-02 v4
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.
Cite
@article{arxiv.0910.3142,
title = {A Dirichlet unit theorem for Drinfeld modules},
author = {Lenny Taelman},
journal= {arXiv preprint arXiv:0910.3142},
year = {2010}
}
Comments
8 pages. (v4: added Thm 2; v3: added conjectural class number formula; v2: minor corrections)