Pure descent for the module of Zariski differentials

Abstract:

It will be shown that for any given pure extension $A \to B$ of noetherian $k$-algebras, with $k$ being a field of characteristic zero, and for any prime ideal $\mathfrak {p} \subseteq A$ the Zariski-Lipman conjecture for ${A_\mathfrak {p}}$ is solvable, if $B$ is a locally factorial domain for which the finite differential module is reflexive. We will also discuss an embedding property with respect to the module of Zariski differentials of ${A_\mathfrak {p}}$.