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Fitting ideals of class groups for CM abelian extensions

Mahiro Atsuta and Takenori Kataoka

Vol. 17 (2023), No. 11, 1901–1924
Abstract

Let K be a finite abelian CM-extension of a totally real field k and T a suitable finite set of finite primes of k. We determine the Fitting ideal of the minus component of the T-ray class group of K, except for the 2-component, assuming the validity of the equivariant Tamagawa number conjecture. As an application, we give a necessary and sufficient condition for the Stickelberger element to lie in that Fitting ideal.

Keywords
class groups, Fitting ideals, CM-fields, equivariant Tamagawa number conjecture
Mathematical Subject Classification
Primary: 11R29
Milestones
Received: 13 December 2021
Revised: 25 December 2022
Accepted: 13 February 2023
Published: 3 October 2023
Authors
Mahiro Atsuta
Institute for Mathematics and Computer Science
Tsuda University
Tokyo
Japan
Takenori Kataoka
Department of Mathematics, Faculty of Science Division II
Tokyo University of Science
Tokyo
Japan

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