Hilbert towers of cubic cyclic extensions of \(\mathbb{Q}\)
type: Item
instance of: scholarly article
title: Hilbert towers of cubic cyclic extensions of \(\mathbb{Q}\)
zbMATH Open document ID: 0872.11048
DOI: 10.1007/BF02678196
author: Christian Maire
published in: Manuscripta Mathematica
publication date: 1997-05-28T00:00:00Z
full work available at URL: https://eudml.org/doc/156267
review text: Using a homological approach to class field towers due to \textit{R. Schoof} [J. Reine Angew. Math. 372, 209-220 (1986; Zbl 0589.12011)], the author gives a sharpening of a criterion for infinite \(p\)-towers over a cubic cyclic extension of the rationals. The main result is that for a prime \(p\), different from 2 or 3, and cyclic cubic \(k/ {\mathbb Q}\), if the \(p\)-rank of the class group of \(k\) is at least 4, then \(k\) admits an infinite \(p\)-class field tower. This improves the Golod-Shafarevich result applied to this case, where the rank is required to be at least 6.
Mathematics Subject Classification ID: 11R37
Mathematics Subject Classification ID: 11R20
zbMATH DE Number: 1002956
zbMATH Keywords: class field towers
zbMATH Keywords: cubic extensions
reviewed by: Thomas A. Schmidt
MaRDI profile type: Publication
cites work: Méthodes et algorithmes pour le calcul numérique du nombre de classes et de unités des extensions cubiques cycliques de Q.
cites work: Q5619167
cites work: Zum Satz von GOLOD‐SCHAFAREWITSCH
cites work: On 2-class field towers of imaginary quadratic number fields
cites work: Infinite class field towers of quadratic fields.
cites work: Q5558003
description: scientific article; zbMATH DE number 1002956