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Jaulent, Jean-François

La théorie de Kummer et le \(K_ 2\) des corps de nombres. (Kummer theory and \(K_ 2\) of number fields). (French) Zbl 0723.11051

Sémin. Théor. Nombres Bordx., Sér. II 2, No. 2, 377-411 (1990).
The interpretation of the \(K_ 2\) of a number field, of the tame and the wild kernel in terms of Kummer theory via Kummer radicals was studied to a great extent by the author in his thesis, based upon earlier work of Tate, Coates and others. In the present paper the author develops a conceptual parallel for the description of genera, which yields a convenient framework for the study of various Tate-twisted Galois modules occurring in Iwasawa theory. In particular, the author reveals the close connection between results about \(K_ 2\) and the Conjectures of Leopoldt and Gross.
Reviewer: M.Kolster (Hamilton / Ontario)

Cited in 1 Review
Cited in 7 Documents

MSC:

11R23 Iwasawa theory
11R70 \(K\)-theory of global fields

Keywords:

genus theory; \(K_ 2\) of a number field; Kummer radicals; genera; Iwasawa theory; Conjectures of Leopoldt and Gross
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\textit{J.-F. Jaulent}, Sémin. Théor. Nombres Bordx., Sér. II 2, No. 2, 377--411 (1990; Zbl 0723.11051)
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References:

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