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Zbl 0723.11051
Jaulent, Jean-François
La théorie de Kummer et le $K\sb 2$ des corps de nombres. (Kummer theory and $K\sb 2$ of number fields). (French)
[J] Sémin. Théor. Nombres Bordx., Sér. II 2, No.2, 377-411 (1990). ISSN 0989-5558

The interpretation of the $K\sb 2$ 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 $K\sb 2$ and the Conjectures of Leopoldt and Gross.
[M.Kolster (Hamilton / Ontario)]

MSC 2000:: *11R23 Iwasawa theory
11R70 K-theory of global fields

Keywords: genus theory; $K\sb 2$ of a number field; Kummer radicals; genera; Iwasawa theory; Conjectures of Leopoldt and Gross

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