Is every extension of \(\mathbb{Q}\) the specialization of a branched covering?
type: Item
instance of: scholarly article
title: Is every extension of \(\mathbb{Q}\) the specialization of a branched covering?
zbMATH Open document ID: 0802.12003
author: Sybilla Beckmann
published in: Journal of Algebra
publication date: 1994-12-15T00:00:00Z
review text: It is shown that every Galois extension of the rationals with symmetric group \(S_ n\) can be obtained as a specialization of a suitable model of a Galois branched covering \({\mathcal C}\to P^ 1\) with the same Galois group, having at most \(2n-1\) branch points. (Here \({\mathcal C}\) is a connected complete and smooth curve over the complex field.) A similar result is obtained for finite abelian extensions of any number field. The proof is based on the work of \textit{D. Saltman} [Adv. Math. 43, 250-283 (1982; Zbl 0484.12004)].
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 11R32
Mathematics Subject Classification ID: 12F12
Mathematics Subject Classification ID: 14E20
zbMATH DE Number: 562445
zbMATH Keywords: branched covering
zbMATH Keywords: Galois group
reviewed by: Władysław Narkiewicz
MaRDI profile type: Publication
full work available at URL: jabr.1994.1068
OpenAlex ID: W2086202578
DOI: 10.1006/JABR.1994.1068
description: scientific article; zbMATH DE number 562445