A class formula for admissible Anderson modules

Bruno Angles (1) , Tuan Ngo Dac (2, 3) , Floric Tavares-Ribeiro (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 ICJ - Institut Camille Jordan
3 CNRS - Centre National de la Recherche Scientifique

In 2012 Taelman proved a class formula for Drinfeld F_q[θ]-modules. For an arbitrary coefficient ring A, several deep but partial results in the direction of a class formula for Drinfeld A-modules have been obtained. In this paper, using a completely new approach based on the notion of Stark units, we establish the class formula for Drinfeld A-modules in full generality. Further we extend this class formula for A-finite Anderson modules and more generally for admissible Anderson modules.

Domaines: Mathématiques [math]; Théorie des nombres [math.NT]

Bruno Angles, Tuan Ngo Dac, Floric Tavares-Ribeiro. A class formula for admissible Anderson modules. 2020. ⟨hal-02490566v1⟩