Stickelberger ideals and Fitting ideals of class groups for abelian number fields
โ Scribed by Masato Kurihara; Takashi Miura
- Publisher
- Springer
- Year
- 2010
- Tongue
- English
- Weight
- 338 KB
- Volume
- 350
- Category
- Article
- ISSN
- 0025-5831
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๐ SIMILAR VOLUMES
It is well-known that in the cyclotomic number field Q(`pn) of prime power conductor, where `pn=exp(2?iร p n ), the index of cyclotomic units in the total unit group is equal to the class number of its maximal real subfield, which is due to Kummer. On the other hand, in 1962 Iwasawa [Iw] showed that
For a totally real field of prime power conductor, we determine the Fitting ideal over the Galois group ring of the ideal class group and of the narrow ideal class group. 1998 Academic Press ## 1. Introduction In this paper we prove a structure result on the ideal class group and on the narrow id
Let K be a real abelian number field satisfying certain conditions and K n the n th layer of the cyclotomic Z p -extension of K. We study the relation between the p-Sylow subgroup of the ideal class group and that of the unit group module the cyclotomic unit group of K n . We give certain sufficient