Stark units in positive characteristic

Bruno Anglès (1) , Tuan Ngo Dac (2, 1) , Floric Tavares Ribeiro (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 CNRS - Centre National de la Recherche Scientifique

We show that the module of Stark units associated to a sign-normalized rank one Drinfeld module can be obtained from Anderson's equi-variant A-harmonic series. We apply this to obtain a class formulà a la Tael-man and to prove a several variable log-algebraicity theorem, generalizing An-derson's log-algebraicity theorem. We also give another proof of Anderson's log-algebraicity theorem using shtukas and obtain various results concerning the module of Stark units for Drinfeld modules of arbitrary rank.

Domaines: Mathématiques [math]

Bruno Anglès, Tuan Ngo Dac, Floric Tavares Ribeiro. Stark units in positive characteristic. Proceedings of the London Mathematical Society, 2017, 115 (4), pp.763-812. ⟨10.1112/plms.12051⟩. ⟨hal-01404894⟩