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Exponents of the ideal class groups of CM number fields

✍ Scribed by S. Louboutin; R. Okazaki


Publisher
Springer-Verlag
Year
2003
Tongue
French
Weight
103 KB
Volume
243
Category
Article
ISSN
0025-5874

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πŸ“œ SIMILAR VOLUMES


CM-Fields with Cyclic Ideal Class Groups
✍ StΓ©phane Louboutin πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 298 KB

We prove that there are only finitely many CM-fields N with cyclic ideal class groups of 2-power orders such that the complex conjugation is the square of some automorphism of N. Since their actual determination would be too difficult, we only content ourselves with the determination of the nonquadr

A Riemann-Hurwitz Formula for thep-Rank
✍ Kay Wingberg πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 486 KB

In this note we prove an analogue of the classical Riemann-Hurwitz formula for the minus part of the p-rank of S-ideal class groups of algebraic CM-fields. The result is an improvement of Kida's formula for the cyclotomic Z p -extension.