An application of Tarski's principle to absolute Galois groups of function fields
type: Item
instance of: scholarly article
title: An application of Tarski's principle to absolute Galois groups of function fields
zbMATH Open document ID: 0645.12009
DOI: 10.1016/0168-0072(87)90076-5
author: Paulo Ribenboim
author: Lou van den Dries
published in: Annals of Pure and Applied Logic
publication date: 1987-01-01T00:00:00Z
review text: In this paper the authors reprove Douady's result that the absolute Galois group of the rational function field C(t) over an algebraically closed field C of characteristic zero is the free profinite group generated by the set C. In the paper of \textit{A. Douady} [C. R. Acad. Sci., Paris 258, 5305-5308 (1964; Zbl 0146.421)] the essential ingredient is the `change of base field' from \({\mathbb{C}}\) to C provided by Grothendieck's `profinite fundamental group functor'. The authors instead use model theoretic methods in order to transfer the classical result for \({\mathbb{C}}(t)\) to C(t). They also treat in a similar manner the case of the absolute Galois group of the rational function field R(t) where R is any real closed field. They use model theoretic methods (like the Tarski principle) in order to transfer the result for \({\mathbb{R}}(t)\) [obtained by \textit{W. Krull} and \textit{J. Neukirch} in Math. Ann. 193, 197-209 (1971; Zbl 0236.12104)] to the case of R(t).
reviewed by: Alexander Prestel
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 12L10
Mathematics Subject Classification ID: 14H05
Mathematics Subject Classification ID: 11R58
Mathematics Subject Classification ID: 14Pxx
zbMATH DE Number: 4051762
zbMATH Keywords: transfer principle
zbMATH Keywords: absolute Galois group of the rational function field
zbMATH Keywords: real closed field
zbMATH Keywords: Tarski principle
MaRDI profile type: Publication
full work available at URL: 0168-0072(87)90076-5
OpenAlex ID: W2040868128
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description: scientific article; zbMATH DE number 4051762