Finite Cohen-Macaulay type and smooth non-commutative schemes

Abstract

A commutative local Cohen-Macaulay ring R of finite Cohen-Macaulay type is known to be an isolated singularity; that is, Spec(R) \ {m} is smooth. This paper proves a non-commutative analogue. Namely, if A is a (non-commutative) graded Artin-Schelter Cohen-Macaulay algebra which is fully bounded Noetherian and has finite Cohen-Macaulay type, then the non-commutative projective scheme determined by A is smooth. ©Canadian Mathematical Society 2008.