Pure descent for the module of Zariski differentials

Abstract

It will be shown that for any given pure extension A → B A \to B of noetherian k k -algebras, with k k being a field of characteristic zero, and for any prime ideal p ⊆ A \mathfrak {p} \subseteq A the Zariski-Lipman conjecture for A p {A_\mathfrak {p}} is solvable, if B 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 p {A_\mathfrak {p}} .