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

Soient K un corps abélien réel, ℓ un nombre premier, premier à [K:Q] et Y n le quotient du groupe des unités semi-locales de K(1 ℓ 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.

Let K an abelian number field, ℓ a prime number, prime to [K:Q], Y n the quotient of the group of semi-local units in K(1 ℓ 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.

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

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