Contribution of the study of Gras conjecture and Iwasawa’s main conjecture, by Euler systems
type: Dataset
description: The goal of this work is to show how Euler systems allows us to compare, for some abelian extensions, the Galois module of global units modulo Stark units with the Galois module of ideal p-classes. We restricts ourselves to abelian extensions over a base field k which can be an imaginary quadratic field or a global field of positive characteristic. The Gras conjecture predicts that for all finite abelian extension K/k, all prime number p not dividing [K : k], and all irreducible and nontrivial Qp-character ψ of Gal (K/k), the ψ-part of the p-class group of K and the ψ-part of the group of global units modulo Stark units have the same cardinal. First we prove a weak form of the conjecture, and then we use Euler systems to extend the results obtained among others by Rubin, Xu et Zhao. Then we assume that k is an imaginary quadratic field, and we consider a special Zp-extension k∞ of k, where p is a prime number different from 2 and 3, decomposed in k. We prove that for all finite extension K∞ of k∞ abelian over k, and for all irreducible Cp-character χ of the torsion subgroup of Gal(K∞/k), the characteristic ideal of the χ-quotients of the module of p-classes and the characteristic ideal of the module of global units modulo Stark units are the same. It is one of the versions of the main conjecture in Iwasawa theory, which extends a result of Rubin and Bley. It is also a step for a further work, where we extend a result of Rubin on the two variables main conjecture
identifier: NNT: 2011BESA2026
issued: 2026-05-10T12:39:04.198565
language: fr
modified: 2026-05-10T12:39:04.198570
contact point: Organization
  fn: CCSD
keyword: class-field-theory
keyword: class-group
keyword: conjecture-de-gras
keyword: drinfeld-modules
keyword: elliptic-units
keyword: euler-systems
keyword: gras-conjecture
keyword: groupe-de-classes
keyword: infoeu-reposemanticsdoctoralthesis
keyword: iwasawa-theory
keyword: mathmath-dsmathematics-mathdynamical-systems-mathds
keyword: modules-de-drinfeld
keyword: stark-units
keyword: systemes-deuler
keyword: theorie-diwasawa
keyword: theorie-du-corps-de-classe
keyword: theses
keyword: unites-de-stark
keyword: unites-elliptiques
landing page: https://theses.hal.science/tel-00839919

Contribution of the study of Gras conjecture and Iwasawa’s main conjecture, by Euler systems
type: Distribution
format: HTML
issued: 2026-05-10T12:39:04.225580
modified: 2026-05-10T12:39:04.182598
access URL: https://theses.hal.science/tel-00839919

test_moissonnage_selune
type: Agent