A class formula for admissible Anderson modules

International audienceIn 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 or abelian Anderson modules and more generally for admissible Anderson modules