Formules de classes pour les corps abéliens réels
[Class formulae for real abelian fields]
Annales de l'Institut Fourier, Volume 51 (2001) no. 4, pp. 903-937.

We show p-adic and “character by character” refinements of Sinnott’s index formula for a totally real abelian number field. Such refinements have also been obtained by Kuz’min by different methods (but see comments in the introduction). Applications are given to Iwasawa theory of semi-local units and cyclotomic units.

Nous montrons des raffinements p-adique et “caractères par caractères” de la formule d’indice de Sinnott pour un corps abélien totalement réel. De tels raffinements ont aussi été obtenus par Kuz’min avec des méthodes différentes (voir les commentaires en introduction). Nous donnons des applications à la théorie d’Iwasawa des unités semi- locales et cyclotomiques.

DOI: 10.5802/aif.1840
Classification: 11R23,  11R29,  11R18
Keywords: class groups, p-adic L functions, Iwasawa’s theory
Belliard, Jean-Robert 1; Nguyen Quang Do, Thong 1

1 Université de Franche-Comté, Laboratoire de Mathématiques, CNRS UMR 6623, 16 route de Gray, 25030 Besançon Cedex (France)
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Belliard, Jean-Robert; Nguyen Quang Do, Thong. Formules de classes pour les corps abéliens réels. Annales de l'Institut Fourier, Volume 51 (2001) no. 4, pp. 903-937. doi : 10.5802/aif.1840. http://www.numdam.org/articles/10.5802/aif.1840/

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