Soutenance de Thèse de Daniel KRELL CALVO

Titre : Arithmetic of Anderson t-modules at finite places

Résumé: In 2020, Anglès, Ngo Dac and Tavares-Ribeiro proved, for a family of Anderson t-modules, a variant of the class formula, which we call the reduced class formula. In this thesis, we prove a P-adic version of this reduced class formula. As a consequence, we deduce some vanishing properties of the P-adic versions of several well-known L-series, including Carlitz zeta values, Pellarin L-series and Dirichlet-Goss L-series.