Fitting ideals of class groups for CM abelian extensions

IF 0.9 1区数学 Q2 MATHEMATICS

Algebra & Number Theory Pub Date : 2023-10-03 DOI:10.2140/ant.2023.17.1901

Mahiro Atsuta, Takenori Kataoka

引用次数: 1

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.

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CM交换扩展的类群的拟合法

设K是全实域K的有限阿贝尔CM扩张，T是K的有限素数的适当有限集。假定等变Tamagawa数猜想的有效性，我们确定了除2-分量外的K的T-射线类群的负分量的拟合理想。作为一个应用，我们给出了Stickelberger元素位于Fitting理想中的一个充要条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebra & Number Theory MATHEMATICS-

CiteScore

1.80

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： ANT’s inclusive definition of algebra and number theory allows it to print research covering a wide range of subtopics, including algebraic and arithmetic geometry. ANT publishes high-quality articles of interest to a broad readership, at a level surpassing all but the top four or five mathematics journals. It exists in both print and electronic forms. The policies of ANT are set by the editorial board — a group of working mathematicians — rather than by a profit-oriented company, so they will remain friendly to mathematicians'' interests. In particular, they will promote broad dissemination, easy electronic access, and permissive use of content to the greatest extent compatible with survival of the journal. All electronic content becomes free and open access 5 years after publication.