Unités cyclotomiques, unités semi-locales et -extensions. II
Annales de l'Institut Fourier, Volume 29 (1979) no. 4, pp. 1-15.

Let K an abelian number field, a prime number, prime to [K:Q], Y n the quotient of the group of semi-local units in K(1 n ) by the group of cyclotomic units. By giving the Galois structure of lim Y n , we generalise a theorem of Iwasawa and use this result for comparing classical conjectures about projective limits of class groups.

Soient K un corps abélien réel, un nombre premier, premier à [K:Q] et Y n le quotient du groupe des unités semi-locales de K(1 n ) par celui des unités cyclotomiques : on donne la structure galoisienne de la limite projective des Y n , généralisant un théorème d’Iwasawa, et on applique ceci à la comparaison de conjecture classique sur la limite projective des groupes de classes.

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Gillard, Roland. Unités cyclotomiques, unités semi-locales et ${\mathbb {Z}}_\ell $-extensions. II. Annales de l'Institut Fourier, Volume 29 (1979) no. 4, pp. 1-15. doi : 10.5802/aif.763. http://www.numdam.org/articles/10.5802/aif.763/

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