TY - JOUR
T1 - Finite Cohen-Macaulay type and smooth non-commutative schemes
AU - Jørgensen, Peter
PY - 2008/4
Y1 - 2008/4
N2 - 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.
AB - 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.
KW - Artin-Schelter Cohen-Macaulay algebra
KW - Artin-Schelter Gorenstein algebra
KW - Auslander's theorem on finite Cohen-Macaulay type
KW - Cohen-Macaulay ring
KW - Fully bounded Noetherian algebra
KW - Isolated singularity
KW - Maximal Cohen-Macaulay module
UR - http://www.scopus.com/inward/record.url?scp=42549124218&partnerID=8YFLogxK
U2 - 10.4153/cjm-2008-018-0
DO - 10.4153/cjm-2008-018-0
M3 - Journal article
AN - SCOPUS:42549124218
SN - 0008-414X
VL - 60
SP - 379
EP - 390
JO - Canadian Journal of Mathematics
JF - Canadian Journal of Mathematics
IS - 2
ER -