Conjecture principale équivariante, idéaux de Fitting et annulateurs en théorie d’Iwasawa

Thong Nguyen Quang Do[1]

  • [1] UMR 6623 CNRS Université de Franche-Comté 16, Route de Gray 25030 Besançon Cedex - France

Journal de Théorie des Nombres de Bordeaux (2005)

  • Volume: 17, Issue: 2, page 643-668
  • ISSN: 1246-7405

Abstract

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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 ℤ p [ [ G ∞ ] ] , where G ∞ = G a l ( K ∞ / k ) , K ∞ being the cyclotomic ℤ 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.

How to cite

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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 17.2 (2005): 643-668. <http://eudml.org/doc/249463>.

@article{NguyenQuangDo2005,
abstract = {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 $\mu _p$) pour calculer l’idéal de Fitting d’un certain module d’Iwasawa sur l’algèbre complète $\{\mathbb\{Z\}\}_\{p\}[[G_\{\infty \}]],$ où $G_\{\infty \} = \ Gal\ (K_\{\infty \}/k)$ et $K_\{\infty \}$ est la $\{\mathbb\{Z\}\}_\{p\}$-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},
affiliation = {UMR 6623 CNRS Université de Franche-Comté 16, Route de Gray 25030 Besançon Cedex - France},
author = {Nguyen Quang Do, Thong},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Fitting ideals; Equivariant Main Conjecture; Main conjecture; cohomology},
language = {fre},
number = {2},
pages = {643-668},
publisher = {Université Bordeaux 1},
title = {Conjecture principale équivariante, idéaux de Fitting et annulateurs en théorie d’Iwasawa},
url = {http://eudml.org/doc/249463},
volume = {17},
year = {2005},
}

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
PB - Université Bordeaux 1
VL - 17
IS - 2
SP - 643
EP - 668
AB - 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 $\mu _p$) pour calculer l’idéal de Fitting d’un certain module d’Iwasawa sur l’algèbre complète ${\mathbb{Z}}_{p}[[G_{\infty }]],$ où $G_{\infty } = \ Gal\ (K_{\infty }/k)$ et $K_{\infty }$ est la ${\mathbb{Z}}_{p}$-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
LA - fre
KW - Fitting ideals; Equivariant Main Conjecture; Main conjecture; cohomology
UR - http://eudml.org/doc/249463
ER -

References

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