A Dirichlet unit theorem for Drinfeld modules

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.

8 pages. (v4: added Thm 2; v3: added conjectural class number formula; v2: minor corrections)

Cited by in corpus (14)

• Special L-values of Drinfeld modules
• Arithmetic of positive characteristic L-series values in Tate algebras
• Arithmetic of characteristic p special L-values (with an appendix by V. Bosser)
• Explicit Formulae for $L$-values in Positive Characteristic
• The de Rham isomorphism for Drinfeld modules over Tate algebras
• Shtuka cohomology and special values of Goss L-functions
• Log-algebraic identities on Drinfeld modules and special L-values
• The Carlitz shtuka
• The Spiegelungssatz for the Carlitz module
• Arithmetic of function field units
• Special functions and twisted $L$-series
• Arithmetic of Units in F_q[T]
• A Spiegelungssatz for function field $L$-series
• On equivariant class formulas for t-modules