Class groups of abelian fields, and the main conjecture
type: Item
instance of: scholarly article
title: Class groups of abelian fields, and the main conjecture
zbMATH Open document ID: 0729.11053
author: Cornelius Greither
publication date: 1992-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74963
review text: The first part of this paper gives a proof of the main conjecture of Iwasawa theory for abelian base fields, including the case \(p=2\), by Kolyvagin's method of Euler systems. On the way, one obtains a general result on local units modulo circular units. This is then used to deduce theorems on the order of \(\chi\)-parts of p-class groups of abelian number fields: first for relative class groups as has been done recently by Solomon for odd p, and second for class groups of real fields (again including the case \(p=2)\). As a consequence, a generalization of the Gras conjecture is stated and proved.
reviewed by: Cornelius Greither
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11R42
Mathematics Subject Classification ID: 11R20
Mathematics Subject Classification ID: 11R18
Mathematics Subject Classification ID: 11R27
zbMATH DE Number: 4204471
zbMATH Keywords: cyclotomic extensions
zbMATH Keywords: p-adic L-functions
zbMATH Keywords: main conjecture of Iwasawa theory
zbMATH Keywords: units
zbMATH Keywords: abelian number fields
zbMATH Keywords: relative class groups
zbMATH Keywords: class groups of real fields
zbMATH Keywords: Gras conjecture
Wikidata QID: Q123346341
MaRDI profile type: Publication
OpenAlex ID: W2020538849
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DOI: 10.5802/AIF.1299
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 4204471