Généralisation d'un Théorème d'Iwasawa

Jean-François Jaulent (1)

1 IMB - Institut de Mathématiques de Bordeaux

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.

Mots clés: Iwasawa theory; Iwasawa invariants

Domaines: Théorie des nombres [math.NT]

Jean-François Jaulent. Généralisation d'un Théorème d'Iwasawa. Journal de Théorie des Nombres de Bordeaux, 2005, 17, pp.527--553. ⟨hal-00202454v2⟩