Sur la 2-Extension Maximale Non Ramifiée de la Z2-Extension Cyclotomique de Certains Corps Quadratiques

Mouhib, Ali

doi:10.2478/auom-2014-0016

Abstract

Soient ℓ et ℓ' deux nombres premiers distincts, k = Q(√ℓℓ') et k_∞ la Z₂-extension cyclotomique de k. Soient L_∞ la 2-extension maximale non ramifiée sur k_∞ et L_∞ la sous-extension abélienne maximale de L_∞/k_∞. Sous certaines conditions sur les premiers ℓ et ℓ', nous etudions la structure des groupes de Galois Gal(L_∞/k_∞) et Gal(L_∞/k_∞).

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Sur la 2-Extension Maximale Non Ramifiée de la Z2-Extension Cyclotomique de Certains Corps Quadratiques

Abstract

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