Type: Article

On the k-torsion of the module of differentials of order n of hypersurfaces

de Alba, Hernán; Duarte, Daniel;

Abstract:

Let K be a perfect field, A=K[X1,…,Xs]/(f), where f is an irreducible polynomial, and let R be the local ring of a closed point P of Spec(A). The main result of this paper is that, for a fixed natural number k?1, A is non-singular in codimension k at P if and only if ?(n)R/K is k-torsion-free.