TY - JOUR
T1 - Stickelberger ideals and Fitting ideals of class groups for abelian number fields
AU - Kurihara, Masato
AU - Miura, Takashi
PY - 2011/7
Y1 - 2011/7
N2 - 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 (Invent Math 76:179-330, 1984) up to the 2-component, and proves Conjecture 0. 1 in Kurihara (J Reine Angew Math 561:39-86, 2003). We also study Brumer's conjecture and prove a stronger version for a CM-field, assuming certain conditions, in particular on the Galois group.
AB - 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 (Invent Math 76:179-330, 1984) up to the 2-component, and proves Conjecture 0. 1 in Kurihara (J Reine Angew Math 561:39-86, 2003). We also study Brumer's conjecture and prove a stronger version for a CM-field, assuming certain conditions, in particular on the Galois group.
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U2 - 10.1007/s00208-010-0570-y
DO - 10.1007/s00208-010-0570-y
M3 - Article
AN - SCOPUS:79958217026
SN - 0025-5831
VL - 350
SP - 549
EP - 575
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 3
ER -