Cyclotomic Units in Zp-Extensions
β Scribed by R. Kucera; J. Nekovar
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 532 KB
- Volume
- 171
- Category
- Article
- ISSN
- 0021-8693
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π SIMILAR VOLUMES
Let p be an odd prime number, K an imaginary abelian field with z p 2 K Γ ; and K 1 =K the cyclotomic Z p -extension with its nth layer K n : In the previous paper, we showed that for any n and any unramified cyclic extension L=K n of degree p; LK nΓΎ1 =K nΓΎ1 does have a normal integral basis (NIB) e
Fix an odd prime number p and an abelian field K. Let U (resp. C) be the projective limit of the semi-local units at p (resp. of the cyclotomic units) of each intermediate field of the cyclotomic Z p -extension K ΓK. We study the Galois module structure of UΓC. We generalize results of Iwasawa and G