Arithmetic of positive characteristic L-series values in Tate algebras

作者：Angles B^*; Pellarin F^*; Ribeiro F Tavares^*; Demeslay F^*

来源：Compositio Mathematica, 2016, 152(1): 1-61.

DOI：10.1112/S0010437X15007563

• L-values in positive characteristic
• log-algebraic theorem
• class modules
• Bernoulli-Carlitz fractions

The second author has recently introduced a new class of L-series in the arithmetic theory of function fields over finite fields. We show that the values at one of these L-series encode arithmetic information of a generalization of Drinfeld modules defined over Tate algebras that we introduce (the coefficients can be chosen in a Tate algebra). This enables us to generalize Anderson's log-algebraicity theorem and an analogue of the Herbrand-Ribet theorem recently obtained by Taelman.

• 出版日期2016-1