Principe d'Oka-Grauert dans \(A^{\infty}\). (The Oka-Grauert principle in \(A^{\infty})\)
type: Item
instance of: scholarly article
title: Principe d'Oka-Grauert dans \(A^{\infty}\). (The Oka-Grauert principle in \(A^{\infty})\)
zbMATH Open document ID: 0699.32009
DOI: 10.1007/BF01215159
author: Ahmed Sebbar
published in: Mathematische Zeitschrift
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174073
review text: On a domain \(\Omega\) of \({\mathbb{C}}^ n\), let \(A^ k(\Omega)\) be the space of holomorphic functions which are \(C^ k\) on \({\bar \Omega}\) and \(A^{\infty}(\Omega)\) the intersection of the \(A^ k(\Omega)'s\), \(k\in {\mathbb{N}}\). Let \(A^{\infty}\) be the corresponding sheaf of germs on \({\bar \Omega}\). The author investigates the validity of the Oka-Grauert principle in the \(A^{\infty}\) framework. The main results are a version of Cartan's A and B theorems for \(A^{\infty}\)-coherent sheaves and a Grauert type theorem in the \(A^{\infty}\) case: if \(\Omega\) is pseudoconvex with \(C^{\infty}\) boundary, an \(A^{\infty}\) fibre bundle over \({\bar \Omega}\) is \(A^{\infty}\) trivial if and only if it is topologically trivial.
reviewed by: Guy Roos
Mathematics Subject Classification ID: 32E35
Mathematics Subject Classification ID: 32A38
Mathematics Subject Classification ID: 32L10
zbMATH DE Number: 4146392
zbMATH Keywords: Cartan A theorem
zbMATH Keywords: Cartan B theorem
zbMATH Keywords: Oka-Grauert principle
zbMATH Keywords: \(A^{\infty }\)-coherent sheaves
zbMATH Keywords: Grauert type theorem
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4146392