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arXiv · 2104.14765

Fitting ideals of class groups for CM abelian extensions

Mahiro Atsuta·Takenori Kataoka
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Abstract

Let $K/k$ be a finite abelian CM-extension and $T$ a suitable finite set of finite primes of $k$. In this paper, 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.

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Mahiro Atsuta, Takenori Kataoka. 2021-04-30. Fitting ideals of class groups for CM abelian extensions. https://doi.org/10.2140/ant.2023.17.1901

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