Stickelberger ideals and Fitting ideals of class groups for abelian number fields
نویسندگان
چکیده
In this paper, we determine completely the initial Fitting ideal of the minus part of the ideal class group of an abelian number field over Q up to the 2-component. This answers an open question of Mazur and Wiles [11] up to the 2-component, and proves Conjecture 0.1 in [8]. We also study Brumer’s conjecture and prove a stronger version for a CM-field, assuming certain conditions, in particular on the Galois group.
منابع مشابه
On the Structure of Ideal Class Groups of CM - Fields dedicated to Professor K . Kato on his 50 th birthday
For a CM-field K which is abelian over a totally real number field k and a prime number p, we show that the structure of the χ-component AχK of the p-component of the class group of K is determined by Stickelberger elements (zeta values) (of fields containing K) for an odd character χ of Gal(K/k) satisfying certain conditions. This is a generalization of a theorem of Kolyvagin and Rubin. We def...
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