Conjecture principale équivariante, idéaux de Fitting et annulateurs en théorie d’Iwasawa
Journal de théorie des nombres de Bordeaux, Volume 17 (2005) no. 2, pp. 643-668.

For an odd prime number p and an abelian extension of totally real number fields K/k, we use the Equivariant Main Conjecture proved by Ritter and Weiss (modulo the vanishing of the μ p invariant) to compute the Fitting ideal of a certain Iwasawa module over the complete group algebra p [[G ]], where G =Gal(K /k), K being the cyclotomic p -extension of K. By descent, this gives the p-part of (a cohomological version of) the Coates-Sinnott conjecture, as well as a weak form of the p-part of the Brumer conjecture.

Pour un nombre premier impair p et une extension abélienne K/k de corps de nombres totalement réels, nous utilisons la Conjecture Principale Équivariante démontrée par Ritter et Weiss (modulo la nullité de l’invariant μ p ) pour calculer l’idéal de Fitting d’un certain module d’Iwasawa sur l’algèbre complète p [[G ]],G =Gal(K /k) et K est la p -extension cyclotomique de K. Par descente, nous en déduisons la p-partie de la version cohomologique de la conjecture de Coates-Sinnott, ainsi qu’une forme faible de la p-partie de la conjecture de Brumer

DOI: 10.5802/jtnb.512
Keywords: Fitting ideals, Equivariant Main Conjecture
Nguyen Quang Do, Thong 1

1 UMR 6623 CNRS Université de Franche-Comté 16, Route de Gray 25030 Besançon Cedex - France
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Nguyen Quang Do, Thong. Conjecture principale équivariante, idéaux de Fitting et annulateurs en théorie d’Iwasawa. Journal de théorie des nombres de Bordeaux, Volume 17 (2005) no. 2, pp. 643-668. doi : 10.5802/jtnb.512. http://www.numdam.org/articles/10.5802/jtnb.512/

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