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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

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.

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

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