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.

中文翻译：

---

CM 阿贝尔扩张的类群拟合理想

让$K$是完全实数域的有限阿贝尔 CM 扩展$k$和$\mathrm{时间}$有限素数的合适有限集合$k$。我们确定负分量的拟合理想$\mathrm{时间}$射线类群$K$，除了$2$-分量，假设等变玉川数猜想的有效性。作为一个应用，我们给出了 Stickelberger 单元处于拟合理想状态的充要条件。