Local Rings of Finite Cohen-Macaulay Type

Abstract

Let (R,m) be a local Cohen-Macaulay ring whosem-adic completionR̂has an isolated singularity. We verify the following conjecture of F.-O. Schreyer:Rhas finite Cohen-Macaulay type if and only ifR̂has finite Cohen-Macaulay type. We also show that the hypersurfacek[[x0,...,xd]]/(f) has finite Cohen-Macaulay type if and only ifks[[x0,...,xd]]/(f) has finite Cohen-Macaulay type, whereksis the separable closure of the fieldk. © 1998 Academic Press.