Généralisation d'un Théorème d'Iwasawa

JAULENT, Jean-François

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JAULENT, Jean-François
Institut de Mathématiques de Bordeaux [IMB]

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Ce document a été publié dans

Journal de Théorie des Nombres de Bordeaux. 2005, vol. 17, p. 527--553

Société Arithmétique de Bordeaux

Résumé en anglais

We extend to convenient finite quotients of a noetherian Lambda-module the classical result of K. Iwasawa giving the asymptotic expression of the l-part of the number of ideal class groups in Zl-extensions of number fields. Then, in the arithmetic context, we compute the three characters associated by this way to the l-groups of T-infinitesimal S-classes in the cyclotomic tower and relate them to the classical invariants and the decomposition characters associated to the finite sets of places S and T. A main tool in this study is the so-called Spiegelungssatz of Georges Gras, which exchanges (wild or tame) ramification and decomposition. The main results of this arithmetical part extend those we obtained with Christian Maire in a previous article. The most intricate study of the wild contribution of the sets S and T involves a generalization of a classical result of R. Greenberg on the genus theory of cyclotomic towers.< Réduire

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