Faisceaux cohérents en géométrie algébrique réelle. (Coherent sheaves in real algebraic geometry)
type: Item
instance of: scholarly article
title: Faisceaux cohérents en géométrie algébrique réelle. (Coherent sheaves in real algebraic geometry)
zbMATH Open document ID: 0586.14020
DOI: 10.1216/RMJ-1984-14-4-981
published in: Rocky Mountain Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: In this short résumé, the author announces a cohomological proof, via A-coherent sheaves, of Efroymson's extension theorem: Let h be a Nash function on \(R^ n\) such that \(h^{-1}(0)\neq \emptyset\) and U a semi- algebraic open set containing \(h^{-1}(0)\). Then for any Nash function \(f: U\to R\), there exists a Nash function \(g: R^ n\to R\) such that \(f- g=kh\), where \(k: U\to R\) is a Nash function. Such a cohomological proof would be very important in the theory of Nash functions. Unfortunately, none of the detailed versions proposed by the author have been fully convincing.
Mathematics Subject Classification ID: 14Pxx
Mathematics Subject Classification ID: 14F99
zbMATH DE Number: 3939503
zbMATH Keywords: coherent sheaves
zbMATH Keywords: Efroymson's extension theorem
zbMATH Keywords: Nash function
reviewed by: Marie-Françoise Roy
MaRDI profile type: Publication
author: Hamet Seydi
description: scientific article; zbMATH DE number 3939503