LOCAL-RINGS OF FINITE COHEN-MACAULAY TYPE

Let (R, m) be a local Cohen-Macaulay ring whose m-adic completion R ha s an isolated singularity. We verify the following conjecture of F.-O. Schreyer: R has finite Cohen-Macaulay type if and only if (R) over ca p 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 t he separable closure of the field k. (C) 1998 Academic Press.