A Riemann-Hurwitz formula for the \(p\)-rank of ideal class groups of CM-fields (Q1912274)
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scientific article; zbMATH DE number 874183
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Riemann-Hurwitz formula for the \(p\)-rank of ideal class groups of CM-fields |
scientific article; zbMATH DE number 874183 |
Statements
A Riemann-Hurwitz formula for the \(p\)-rank of ideal class groups of CM-fields (English)
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6 May 1996
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\textit{Y. Kida} [J. Number Theory 12, 519-528 (1980; Zbl 0455.12007)] proved an analogue of the Riemann-Hurwitz formula for the minus part of the Iwasawa \(\lambda\)-invariant of the cyclotomic \(\mathbb{Z}_p\)-extension of an algebraic number field of CM-type. The author shows that a similar formula is true for the minus part of the \(p\)-rank of an \(S\)-ideal group of a CM-field.
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\(p\)-rank of ideal class groups
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Iwasawa theory
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Riemann-Hurwitz formula
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CM-field
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