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.
Arithmetic of positive characteristic -series values in Tate algebras / Angl(`(e))s, B.; Pellarin, F.; Tavares Ribeiro, F.; Demeslay, F.. - In: COMPOSITIO MATHEMATICA. - ISSN 0010-437X. - 152:1(2015), pp. 1-61. [10.1112/s0010437x15007563]
Arithmetic of positive characteristic -series values in Tate algebras
F. Pellarin;
2015
Abstract
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.File | Dimensione | Formato | |
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