Class number relations of algebraic tori. II (Q1088721)
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scientific article; zbMATH DE number 3991623
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Class number relations of algebraic tori. II |
scientific article; zbMATH DE number 3991623 |
Statements
Class number relations of algebraic tori. II (English)
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1986
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[For part I see the preceding review.] Let K/k be a finite extension of number fields, \(T_ 1\) the kernel of the norm map \(R_{K/k}(G_ m/k)\to G_ m\), and \(T_ 2=G_ m\). Write \(h_ k\), \(h_ K\), \(h_{K/k}\), \(h'_{K/k}\) for the class numbers of k, K, \(T_ 1\), \(T_ 2\), respectively. Put \(E(K/k)=h_ K(h_ k h_{K/k})^{-1}\), \(E'(K/k)=h_ K (h_ k h'_{K/k})^{-1}\). Formulas for E and E' are given in terms of Adamson's non-normal cohomology groups.
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class number
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algebraic torus
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Tamagawa number
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Adamson's non-normal cohomology groups
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