For an odd prime number and an abelian extension of totally real number fields we use the Equivariant Main Conjecture proved by Ritter and Weiss (modulo the vanishing of the invariant) to compute the Fitting ideal of a certain Iwasawa module over the complete group algebra where being the cyclotomic -extension of . By descent, this gives the -part of (a cohomological version of) the Coates-Sinnott conjecture, as well as a weak form of the -part of the Brumer conjecture.
Pour un nombre premier impair et une extension abélienne de corps de nombres totalement réels, nous utilisons la Conjecture Principale Équivariante démontrée par Ritter et Weiss (modulo la nullité de l’invariant ) pour calculer l’idéal de Fitting d’un certain module d’Iwasawa sur l’algèbre complète où et est la -extension cyclotomique de . Par descente, nous en déduisons la -partie de la version cohomologique de la conjecture de Coates-Sinnott, ainsi qu’une forme faible de la -partie de la conjecture de Brumer
@article{JTNB_2005__17_2_643_0, author = {Nguyen Quang Do, Thong}, title = {Conjecture principale \'equivariante, id\'eaux de {Fitting} et annulateurs en th\'eorie {d{\textquoteright}Iwasawa}}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {643--668}, publisher = {Universit\'e Bordeaux 1}, volume = {17}, number = {2}, year = {2005}, doi = {10.5802/jtnb.512}, zbl = {1098.11054}, mrnumber = {2211312}, language = {fr}, url = {http://www.numdam.org/articles/10.5802/jtnb.512/} }
TY - JOUR AU - Nguyen Quang Do, Thong TI - Conjecture principale équivariante, idéaux de Fitting et annulateurs en théorie d’Iwasawa JO - Journal de théorie des nombres de Bordeaux PY - 2005 SP - 643 EP - 668 VL - 17 IS - 2 PB - Université Bordeaux 1 UR - http://www.numdam.org/articles/10.5802/jtnb.512/ DO - 10.5802/jtnb.512 LA - fr ID - JTNB_2005__17_2_643_0 ER -
%0 Journal Article %A Nguyen Quang Do, Thong %T Conjecture principale équivariante, idéaux de Fitting et annulateurs en théorie d’Iwasawa %J Journal de théorie des nombres de Bordeaux %D 2005 %P 643-668 %V 17 %N 2 %I Université Bordeaux 1 %U http://www.numdam.org/articles/10.5802/jtnb.512/ %R 10.5802/jtnb.512 %G fr %F JTNB_2005__17_2_643_0
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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