Iwasawa main conjecture for the Carlitz cyclotomic extension and applications
Anglès, Bruno (Université de Caen. Laboratoire de Mathématiques Nicolas Oresme (France))
Bandini, Andrea (Università degli Studi di Parma. Dipartimento di Matematica e Informatica (Italy))
Bars Cortina, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Longhi, Ignazio (Xi'an Jiaotong-Liverpool University. Department of Mathematical Sciences (China))

Date:	2020
Abstract:	We prove an Iwasawa Main Conjecture for the class group of the p-cyclotomic extension F of the function field Fq(θ) (p is a prime of Fq[θ]), showing that its Fitting ideal is generated by a Stickelberger element. We use this and a link between the Stickelberger element and a p-adic L-function to prove a close analog of the Ferrero-Washington Theorem for F and to provide information on the p-adic valuations of the Bernoulli-Goss numbers β(j) (i. e. , on the values of the Carlitz-Goss ζ-function at negative integers).
Grants:	Ministerio de Economía y Competitividad MTM2016-75980-P
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió sotmesa a revisió
Subject:	Stickelberger series ; Carlitz-Goss ζ-function ; L-functions ; Bernoulli-Goss numbers ; Class groups ; Iwasawa Main Conjecture ; Function fields ; Cyclotomic extensions
Published in:	Mathematische Annalen, Vol. 376, Issue 1-2 (February 2020) , p. 475-523, ISSN 1432-1807

DOI: 10.1007/s00208-019-01875-8

Preprint 36 p, 438.1 KB

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