Local Rings of Finite Cohen–Macaulay Type,

Let (R, m) be a local Cohen–Macaulay ring whosem-adic completionhas an isolated singularity. We verify the following conjecture of F.-O. Schreyer:Rhas finite Cohen–Macaulay type if and only ifhas 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.