Every finitely generated regular field extension has a stable transcendence base
type: Item
instance of: scholarly article
title: Every finitely generated regular field extension has a stable transcendence base
zbMATH Open document ID: 0923.12006
DOI: 10.1007/BF02897065
author: Konrad Neumann
published in: Israel Journal of Mathematics
publication date: 1999-11-01T00:00:00Z
review text: A field \(K\) is called stable if every finitely generated separable field extension \(F\) of \(K\) with \(K\) algebraically closed in \(F\) has a transcendence base \(x_1,\dots,x_n\) such that \(F\) is separable over \(K(x_1, \dots,x_n)\) and \(K\) is algebraically closed in the Galois hull \(\widehat F\) of \(F\) over \(K(x_1, \dots,x_n)\). In this paper it is proved that every field is stable. This generalizes results from [\textit{M. Fried} and \textit{M. Jarden}, Am. J. Math. 100, 653-666 (1976; Zbl 0413.12023), \textit{W.-D. Geyer} and \textit{M. Jarden}, Geom. Dedicata 29, 335-375 (1989; Zbl 0703.12006) and \textit{W.-D. Geyer}, Isr. J. Math. 68, 102-108 (1989; Zbl 0703.12007)]. The author applies the theorem for constructing fields \(K\) for which every absolutely irreducible variety has a least one \(K\)-rational point with some additional properties.
reviewed by: Nicolae Radu
Mathematics Subject Classification ID: 12F20
Mathematics Subject Classification ID: 11R58
Mathematics Subject Classification ID: 14H05
Mathematics Subject Classification ID: 12F10
zbMATH DE Number: 1251449
zbMATH Keywords: stable fields
zbMATH Keywords: function fields
zbMATH Keywords: transcendence base
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02897065
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description: scientific article; zbMATH DE number 1251449