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Displaying similar documents to “Étude du l-groupe des classes des extensions cycliques de degré l”

S -classes infinitésimales d’un corps de nombres algébriques

Jean-François Jaulent (1984)

Annales de l'institut Fourier

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Nous introduisons les notions de nombres et d’idéaux infinitésimaux attachés à un corps de nombres algébriques K relativement à un nombre premier donné , et nous interprétons le groupe de Galois 𝒜 ( K ) de la -extension abélienne -ramifiée maximale de K comme quotient du tensorisé Z Z J ( K ) du groupe des idéaux étrangers à par le sous-module engendré par les idéaux principaux-infinitésimaux. Nous en déduisons diverses conséquences sur l’arithmétique des groupes 𝒜 ( K ) , en montrant en particulier qu’ils...