Principe d'Oka-Grauert dans \(A^{\infty}\). (The Oka-Grauert principle in \(A^{\infty})\)
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.
scientific article; zbMATH DE number 4146392