Local rings of finite Cohen-Macaulay type

Let (R, m) be a local Cohen-Macaulay ring whose m-adic completion R has an isolated singularity. We verify the following conjecture of F.-O. Schreyer: R has finite Cohen-Macaulay type if and only if (R) over cap has finite Cohen-Macaulay type. We also show that the hypersurface k[[x(0),..,x(d)]]/(f) has finite Cohen-Macaulay type if and only if k(s)[[x(0),...,x(d)]]/(f) has finite Cohen-Macaulay type, where k(s) is the separable closure of the field k. (C) 1998 Academic Press.