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

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.


11R23 Iwasawa theory
11R70 \(K\)-theory of global fields
Full Text: DOI Numdam EuDML


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