Greenberg's conjecture and Leopoldt's conjecture
type: Item
instance of: scholarly article
title: Greenberg's conjecture and Leopoldt's conjecture
zbMATH Open document ID: 0971.11053
author: Norikazu Kubotera
published in: Proceedings of the Japan Academy. Series A
publication date: 2001-02-07T00:00:00Z
review text: Let \(p\) be an odd prime number and \(G\) the non-abelian group of order \(p^3\) and exponent \(p\). The author shows there exists Galois extensions \(L\) of \({\mathbb Q}\) with group \(G\) and vanishing Iwasawa invariants \(\lambda,\mu\) and \(\nu\) for the cyclotomic \({\mathbb Z}_p\)-extension of \(L\). He has also a result for extensions \(L/k\) where \(k\) is an imaginary quadratic field with \(p\) a prime not dividing the class number of \(k \) and furthermore unramified in \(k\) if \(p=3\); he proves the existence of such extensions \(L/k\) verifying Leopoldt's conjecture. For this he uses an old criterion found by \textit{H. Miki} [J. Number Theory 26, 117-128 (1987; Zbl 0621.12009)].
reviewed by: Roland Gillard
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 11R27
zbMATH DE Number: 1561770
zbMATH Keywords: Iwasawa theory
zbMATH Keywords: Greenberg's conjecture
zbMATH Keywords: Galois extensions
zbMATH Keywords: cyclotomic \({\mathbb Z}_p\) extension
zbMATH Keywords: Leopoldt conjecture
MaRDI profile type: Publication
full work available at URL: pjaa.76.108
OpenAlex ID: W2020136037
Wikidata QID: Q123013983
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DOI: 10.3792/PJAA.76.108
description: scientific article; zbMATH DE number 1561770