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.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Taelman, L. A Dirichlet unit theorem for Drinfeld modules. Math. Ann. 348, 899–907 (2010). https://doi.org/10.1007/s00208-010-0506-6
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DOI: https://doi.org/10.1007/s00208-010-0506-6