The tame kernel of \(\mathbb Q(\zeta_5)\) is trivial (Q2792375)
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scientific article; zbMATH DE number 6552630
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The tame kernel of \(\mathbb Q(\zeta_5)\) is trivial |
scientific article; zbMATH DE number 6552630 |
Statements
9 March 2016
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tame kernel
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cyclotomic field
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\(K_2\)
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The tame kernel of \(\mathbb Q(\zeta_5)\) is trivial (English)
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The authors prove the theorem stated in the title of the paper. They adapt the original strategy of \textit{J. Tate} [Lect. Notes Math. 342, 524--527 (1973; Zbl 0284.12004)] for finding a finite list of generators of the tame kernel of a given number field. After much computation, sometimes using GP/Pari, they prove using these methods that the tame kernel of \(F=\mathbb{Q}(\zeta_5)\) is generated by symbols of the form \(\{ u,w\}\) where \(u,w\) are absolute units of \(F\). They finish by showing that all such symbols are trivial.
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