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

@article{AIF_1979__29_4_1_0,
     author = {Gillard, Roland},
     title = {Unit\'es cyclotomiques, unit\'es semi-locales et ${\mathbb {Z}}\_\ell $-extensions. II},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {29},
     number = {4},
     year = {1979},
     pages = {1-15},
     doi = {10.5802/aif.763},
     zbl = {0403.12006},
     mrnumber = {81e:12005b},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1979__29_4_1_0}
}
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/item/AIF_1979__29_4_1_0/

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