Vertical components and flatness of Nash mappings
Let \(f:(X,0)\to(Y,0)\) be a Nash map germ such that \((X,0)\) is a pure dimensionally reduced Nash germ and \((Y,0)\) is smooth of dimension \(n\). It is shown that the flatness of \(f\) is equivalent to the absence of algebraic vertical components, which in turn by a result of Auslander is the same as the torsion freeness of a certain \(n\)th analytic tensor product involving the local rings \({\mathcal O}_{X,0}\) and \({\mathcal O}_{Y,0}\).
scientific article; zbMATH DE number 2092902