Stickelberger series and Main Conjecture for function fields
Bandini, Andrea (Universit'a degli Studi di Pisa. Dipartimento di Matematica)
Coscelli, Edoardo

Date:	2021
Abstract:	Let F be a global function field of characteristic p with ring of integers A and let Φ be a Hayes module on the Hilbert class field HA of F. We prove an Iwasawa Main Conjecture for the Z∞p extension F/F generated by the p-power torsion of Φ (p a prime of A). The main tool is a Stickelberger series whose specialization provides a generator for the Fitting ideal of the class group of F. Moreover we prove that the same series, evaluated at complex or p-adic characters, interpolates the Goss Zeta-function or some p-adic L-function, thus providing the link between the algebraic structure (class groups) and the analytic functions, which is the crucial part of Iwasawa Main Conjecture.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Function fields ; Iwasawa main conjecture ; P-adic l-functions ; Stickel berger series ; Divisor class groups
Published in:	Publicacions matemàtiques, Vol. 65 Núm. 2 (2021) , p. 459-498 (Articles) , ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/390232
DOI: 10.5565/PUBLMAT6522103

40 p, 548.1 KB

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