Geodesic
Finite Cohen–Macaulay Type and Smooth Non-Commutative Schemes
Canadian journal of mathematics, Tome 60 (2008) no. 2, pp. 379-390

Voir la notice de l'article provenant de la source Cambridge University Press

A commutative local Cohen–Macaulay ring $R$ of finite Cohen–Macaulay type is known to be an isolated singularity; that is, $\text{Spec}(R)\backslash \{m\}$ 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.
DOI : 10.4153/CJM-2008-018-0
Mots-clés : 14A22, 16E65, 16W50, Artin–Schelter Cohen–Macaulay algebra, Artin–Schelter Gorenstein algebra, Auslander’s theorem on finite Cohen–Macaulay type, Cohen–Macaulay ring, fully bounded Noetherian algebra, isolated singularity, maximal Cohen–Macaulay module, non-commutative projective scheme, punctured spectrum 
Jørgensen, Peter. Finite Cohen–Macaulay Type and Smooth Non-Commutative Schemes. Canadian journal of mathematics, Tome 60 (2008) no. 2, pp. 379-390. doi: 10.4153/CJM-2008-018-0
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[1] [1] Artin, M. and Zhang, J. J., Noncommutative projective schemes. Adv. Math. 109(1994), no. 2, 228–287. Google Scholar

[2] [2] Auslander, M., Isolated singularities and existence of almost split sequences. In: Representation Theory. II. Lecture Notes in Math. 1178, Springer, Berlin, 1986, pp. 194–242. Google Scholar

[3] [3] Auslander, M., Rational singularities and almost split sequences. Trans. Amer. Math. Soc. 293(1986), no. 2, 511–531. Google Scholar

[4] [4] Brown, K. A., Fully bounded Noetherian rings of finite injective dimension. Quart. J. Math. Oxford 41(1990), no. 161, 1–13. Google Scholar

[5] [5] Goodearl, K. and Warfield, R., An introduction to noncommutative Noetherian rings. London Mathematical Society Student Texts 16, Cambridge University Press, Cambridge, 1989. Google Scholar

[6] [6] Herzog, J., Ringe mit nur endlich vielen Isomorphieklassen von maximalen, unzerlegbaren Cohen-Macaulay-Moduln Math. Ann. 233(1978), no. 1, 21–34. Google Scholar

[7] [7] Huneke, C. and Leuschke, G., Two theorems about maximal Cohen-Macaulay modules. Math. Ann. 324(2002), no. 2, 391–404. Google Scholar

[8] [8] Jørgensen, P., Local cohomology for non-commutative graded algebras. Comm. Algebra 25(1997), no. 2, 575–591. Google Scholar

[9] [9] Jørgensen, P., Non-commutative graded homological identities J. LondonMath. Soc. 57(1998), no. 2, 336–350. Google Scholar

[10] [10] Jørgensen, P. and Zhang, J. J., Gourmet's Guide to Gorensteinness. Adv. Math. 151(2000), no. 2, 313–345. Google Scholar

[11] [11] Mori, I., Homological properties of balanced Cohen-Macaulay algebras. Trans. Amer.Math. Soc. 355(2003), no. 3, 1025–1042. Google Scholar

[12] [12] Năstăsescu, C. and van Oystaeyen, F., Graded Ring Theory. North-Holland Mathematical Library 28, North-Holland Publishing, Amsterdam, 1982. Google Scholar

[13] [13] Stafford, J. T. and Zhang, J. J., Homological properties of (graded) Noetherian PI rings. J. Algebra 168(1994), no. 3, 988–1026. Google Scholar

[14] [14] Van den Bergh, M., Existence theorems for dualizing complexes over non-commutative graded and filtered rings. J. Algebra 195(1997), no. 2, 662–679. Google Scholar

[15] [15] Yekutieli, A., Dualizing complexes over noncommutative graded algebras. J. Algebra 153(1992), no. 1, 41–84. Google Scholar

[16] [16] Zhang, J. J., Twisted graded algebras and equivalences of graded categories. Proc. LondonMath. Soc. 72(1996), no. 2, 281–311. Google Scholar

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