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On étudie une famille de corps réels cycliques de degré 10 liés à la courbe modulaire . Les unités modulaires déterminent un sous-groupe d’unités d’indice fini. Sous certaines conditions, cet indice est égal à 1 ou 5.
Nous étudions les extensions abéliennes d’un corps quadratique imaginaire et discutons les analogues des théorèmes de Mazur et Wiles.
Soit une extension cyclique -primaire d’un corps de nombres . On suppose que est métabélienne sur un sous-corps d’indice dans , pour un étranger à ; on note son groupe de Galois de un relèvement dans du quotient Gal. On étudie la structure galoisienne des groupes de -classes de et on s’intéresse en particulier à leurs -composantes, lorsque parcourt le groupe des caractères -adiques irréductibles de . Le choix d’un générateur convenable dans l’idéal d’augmentation...
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