Nous étudions la -partie des noyaux étales sauvage WK 2i (F ) d'un corps de nombres arbitraire F en liaison avec l'arithmétique des classes logarithmiques. Nous en déduisons notamment des formules de rang, des résultats de périodicité et de réflexion, des caractérisations de la trivialité, ainsi que diverses conséquences.
AbstractWe study the -part of the wild étale kernels WK 2i (F ) of an arbitary number field F for a given prime in connection with the logarithmic -class groups C F . From the logarithmic arithmetic we deduce rank formulas, periodicity and reflection theorems, triviality characterizations and various consequences.
Let p be a prime number and ⌳ the associated Iwasawa algebra. Let M be a noetherian ⌳-module which defines a representation of a finite Galois group G. For a given collection of subgroups of G, we show that relations between idempow x tents of ޑ G yield relations among the degrees of the characteristic power series related to the various submodules of fixed points for each subgroup. This general-Ž . izes former results due to Kani in the case of the genus of algebraic curves , and Ž to Madan and Zimmer for the classical Iwasawa invariant related to ޚ -extenp . sions . The method also gives rise to analogous results for the generalised Selmer group of a p-adic representation associated to the absolute Galois group of a number field. A non-Galois version of these results is also given. ᮊ 1996 Academic Press, Inc.
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