Faisceaux cohérents en géométrie algébrique réelle. (Coherent sheaves in real algebraic geometry) (Q1071836)

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.