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ON IWASAWA THEORY OF RUBIN–STARK UNITS AND NARROW CLASS GROUPS

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  31 October 2018

YOUNESS MAZIGH
YOUNESS MAZIGH*
Affiliation:
Faculté des sciences de Meknès, Département de mathématiques, Université Moulay Ismail, B.P. 11201 Zitoune, Meknès 50000, Maroc e-mail: y.mazigh@edu.umi.ac.ma
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Abstract

Let K be a totally real number field of degree r. Let K∞ denote the cyclotomic -extension of K, and let L∞ be a finite extension of K∞, abelian over K. The goal of this paper is to compare the characteristic ideal of the χ-quotient of the projective limit of the narrow class groups to the χ-quotient of the projective limit of the rth exterior power of totally positive units modulo a subgroup of Rubin–Stark units, for some $\overline{\mathbb{Q}_{2}}$-irreducible characters χ of Gal(L∞/K∞).

MSC classification

Primary: 11R23: Iwasawa theory
Secondary: 11R29: Class numbers, class groups, discriminants 11R42: Zeta functions and $L$-functions of number fields
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 61 , Issue 3 , September 2019 , pp. 673 - 691
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

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