Iwasawa main conjecture for the Carlitz cyclotomic extension and applications

Bruno Anglès; Andrea Bandini; Francesc Bars; Ignazio Longhi

doi:10.1007/s00208-019-01875-8

Iwasawa main conjecture for the Carlitz cyclotomic extension and applications

Bruno Anglès, Andrea Bandini, Francesc Bars, Ignazio Longhi

Department of Mathematics

Research output: Contribution to journal › Article › Research

2 Citations (Scopus)

Abstract

© 2019, Springer-Verlag GmbH Germany, part of Springer Nature. 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).

Original language	English
Journal	Mathematische Annalen
DOIs	https://doi.org/10.1007/s00208-019-01875-8
Publication status	Published - 1 Jan 2019

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title = "Iwasawa main conjecture for the Carlitz cyclotomic extension and applications",

abstract = "{\textcopyright} 2019, Springer-Verlag GmbH Germany, part of Springer Nature. 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).",

author = "Bruno Angl{\`e}s and Andrea Bandini and Francesc Bars and Ignazio Longhi",

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day = "1",

doi = "10.1007/s00208-019-01875-8",

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T1 - Iwasawa main conjecture for the Carlitz cyclotomic extension and applications

AU - Anglès, Bruno

AU - Bandini, Andrea

AU - Bars, Francesc

AU - Longhi, Ignazio

PY - 2019/1/1

Y1 - 2019/1/1

N2 - © 2019, Springer-Verlag GmbH Germany, part of Springer Nature. 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).

AB - © 2019, Springer-Verlag GmbH Germany, part of Springer Nature. 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).

U2 - 10.1007/s00208-019-01875-8

DO - 10.1007/s00208-019-01875-8

M3 - Article

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

ER -