A remark on Boston's question concerning the existence of unramified \(p\)-extensions. II
type: Item
instance of: scholarly article
title: A remark on Boston's question concerning the existence of unramified \(p\)-extensions. II
zbMATH Open document ID: 0877.11059
author: Akito Nomura
published in: Proceedings of the Japan Academy. Series A
publication date: 1997-11-16T00:00:00Z
review text: In a previous paper [\textit{A. Nomura}, J. Number Theory 58, 66-70 (1996; Zbl 0856.11052)]\ the author constructed \(p\)-extensions of number fields \(K\) with degree \((K:\mathbb Q)\) coprime to \(p\) which gave a positive answer to a question of N. Boston. Here, the author constructs a similar family of extensions in the case where \((K:\mathbb Q)\) is divisible by \(p\). As a corollary, he proves that the Fontaine-Mazur conjecture holds for certain \(p\)-extensions of \(\mathbb Q\).
Mathematics Subject Classification ID: 11R37
Mathematics Subject Classification ID: 11R20
zbMATH DE Number: 1022283
zbMATH Keywords: Fontaine-Mazur conjecture
zbMATH Keywords: class field tower
zbMATH Keywords: pro-\(p\)-extensions
reviewed by: Franz Lemmermeyer
MaRDI profile type: Publication
full work available at URL: pjaa.73.10
OpenAlex ID: W2116590491
cites work: Some cases of the Fontaine-Mazur conjecture
cites work: Some cases of the Fontaine-Mazur conjecture. II
cites work: On the growth of \(p\)-class groups in \(p\)-class field towers
cites work: On the existence of unramified p-extensions
cites work: A remark on Boston's question concerning the existence of unramified \(p\)-extensions
DOI: 10.3792/PJAA.73.10
description: scientific article; zbMATH DE number 1022283