Log in :: RSS/Atom Feeds
The Michigan Mathematical Journal

Noncommutative resolutions and rational singularities

J. T. Stafford and M. Van den Bergh

Source: Michigan Math. J. Volume 57 (2008), 659-674.

Primary Subjects: 14A22, 14E15, 16S38
Secondary Subjects: 18G20

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.mmj/1220879430
Digital Object Identifier: doi:10.1307/mmj/1220879430
Mathematical Reviews number (MathSciNet): MR2492474
Zentralblatt MATH identifier: 05604553

References

M. Artin, Wildly ramified $\Bbb Z/2$ actions in dimension two, Proc. Amer. Math. Soc. 52 (1975), 60--64.
Mathematical Reviews (MathSciNet): MR374136
Digital Object Identifier: doi:10.2307/2040100
R. Bezrukavnikov, Noncommutative counterparts of the Springer resolution, Proceedings of the International Congress of Mathematicians, vol. II, pp. 1119--1144, European Mathematical Society, Zürich, 2006.
Mathematical Reviews (MathSciNet): MR2275638
R. Bezrukavnikov and D. B. Kaledin, McKay equivalence for symplectic resolutions of quotient singularities, Tr. Mat. Inst. Steklova 246 (2004), 20--42.
Mathematical Reviews (MathSciNet): MR2101282
A. I. Bondal and D. O. Orlov, Derived categories of coherent sheaves, Proceedings of the International Congress of Mathematicians (Beijing, 2002), vol. II, pp. 47--56, Higher Education Press, Beijing, 2002.
Mathematical Reviews (MathSciNet): MR1957019
Zentralblatt MATH: 0996.18007
------, Semi-orthogonal decompositions for algebraic varieties, preprint, math.AG/950601.
J. F. Boutot, Singularités rationelles et quotients par les groupes réductifs, Invent. Math. 88 (1987), 65--68.
Mathematical Reviews (MathSciNet): MR877006
Digital Object Identifier: doi:10.1007/BF01405091
A. Braun, On symmetric, smooth and Calabi--Yau algebras, J. Algebra 317 (2007), 519--533.
Mathematical Reviews (MathSciNet): MR2362929
Digital Object Identifier: doi:10.1016/j.jalgebra.2007.08.021
T. Bridgeland, Flops and derived categories, Invent. Math. 147 (2002), 613--632.
Mathematical Reviews (MathSciNet): MR1893007
Digital Object Identifier: doi:10.1007/s002220100185
K. A. Brown and C. R. Hajarnavis, Homologically homogeneous rings, Trans. Amer. Math. Soc. 281 (1984), 197--208.
Mathematical Reviews (MathSciNet): MR719665
Digital Object Identifier: doi:10.2307/1999529
JSTOR: links.jstor.org
K. A. Brown, C. R. Hajarnavis, and A. B. MacEacharn, Rings of finite global dimension integral over their centres, Comm. Algebra 11 (1983), 67--93.
Mathematical Reviews (MathSciNet): MR687406
Digital Object Identifier: doi:10.1080/00927878308822837
R.-O. Buchweitz, G. Leuschke, and M. Van den Bergh, Noncommutative desingularization of the generic determinant, in preparation.
H. Cartan and S. Eilenberg, Homological algebra, Princeton Univ. Press, Princeton, NJ, 1956.
Mathematical Reviews (MathSciNet): MR77480
Zentralblatt MATH: 0075.24305
J.-C. Chen, Flops and equivalences of derived categories for threefolds with only terminal Gorenstein singularities, J. Differential Geom. 61 (2002), 227--261.
Mathematical Reviews (MathSciNet): MR1972146
Project Euclid: euclid.jdg/1090351385
C. W. Curtis and I. Reiner, Methods of representation theory I. With applications to finite groups and orders, Wiley, New York, 1981.
Mathematical Reviews (MathSciNet): MR632548
Zentralblatt MATH: 0469.20001
K. De Naeghel and M. Van den Bergh, Ideal classes of three dimensional Artin--Schelter regular algebras, J. Algebra 283 (2005), 399--429.
Mathematical Reviews (MathSciNet): MR2102090
Digital Object Identifier: doi:10.1016/j.jalgebra.2004.06.011
R. M. Fossum, The Noetherian different of projective orders, Bull. Amer. Math. Soc. 72 (1966), 898--900.
Mathematical Reviews (MathSciNet): MR210744
Digital Object Identifier: doi:10.1090/S0002-9904-1966-11607-5
Project Euclid: euclid.bams/1183528337
V. Ginzburg, Calabi--Yau algebras, preprint, math.AG/0612139.
O. Iyama and I. Reiten, Fomin--Zelevinsky mutation and tilting modules over Calabi--Yau algebras, preprint, math.RT/0605136.
Mathematical Reviews (MathSciNet): MR2427009
Digital Object Identifier: doi:10.1353/ajm.0.0011
D. Kaledin, On crepant resolutions of symplectic quotient singularities, Selecta Math. (N.S.) 9 (2003), 529--555.
Mathematical Reviews (MathSciNet): MR2031751
Digital Object Identifier: doi:10.1007/s00029-003-0308-8
------, Derived equivalences by quantization, preprint, math.AG/0504584.
Y. Kawamata, $D$-equivalence and $K$-equivalence, J. Differential Geom. 61 (2002), 147--171.
Mathematical Reviews (MathSciNet): MR1949787
Project Euclid: euclid.jdg/1090351323
D. S. Keeler, D. Rogalski, and J. T. Stafford, Naï ve noncommutative blowing up, Duke Math. J. 126 (2005), 491--546.
Mathematical Reviews (MathSciNet): MR2120116
Digital Object Identifier: doi:10.1215/S0012-7094-04-12633-8
Project Euclid: euclid.dmj/1108155760
G. Kempf, F. Knudsen, D. Mumford, and B. Saint-Donat, Toroidal embeddings I, Lecture Notes in Math., 339, Springer-Verlag, Berlin, 1973.
Mathematical Reviews (MathSciNet): MR335518
Zentralblatt MATH: 0271.14017
F. Knop, Der kanonische Modul eines Invariantenrings, J. Algebra 127 (1989), 40--54.
Mathematical Reviews (MathSciNet): MR1029400
Digital Object Identifier: doi:10.1016/0021-8693(89)90271-8
J. Kollár and S. Mori, Birational geometry of algebraic varieties, Cambridge Tracts in Math., 134, Cambridge Univ. Press, Cambridge, 1998.
Mathematical Reviews (MathSciNet): MR1658959
L. Le Bruyn, M. Van den Bergh, and F. Van Oystaeyen, Graded orders, Birkhäuser, Boston, 1988.
Mathematical Reviews (MathSciNet): MR1003605
J. C. McConnell and J. C. Robson, Noncommutative Noetherian rings, Wiley, Chichester, 1987.
Mathematical Reviews (MathSciNet): MR934572
Zentralblatt MATH: 0644.16008
E. Nauwelaerts and F. Van Oystaeyen, Finite generalized crossed products over tame and maximal orders, J. Algebra 101 (1986), 61--68.
Mathematical Reviews (MathSciNet): MR843690
Digital Object Identifier: doi:10.1016/0021-8693(86)90096-7
J. Rainwater, Global dimension of fully bounded noetherian rings, Comm. Algebra 15 (1987), 2143--2156.
Mathematical Reviews (MathSciNet): MR909958
Digital Object Identifier: doi:10.1080/00927878708823527
I. Reiner, Maximal orders, London Math. Soc. Monogr. (N.S.), 5, Academic Press, London, 1975.
L. Silver, Tame orders, tame ramification and Galois cohomology, Illinois J. Math. 12 (1968), 7--34.
Mathematical Reviews (MathSciNet): MR240092
J. T. Stafford and J. J. Zhang, Homological properties of (graded) Noetherian PI rings, J. Algebra 168 (1994), 988--1026.
Mathematical Reviews (MathSciNet): MR1293638
Digital Object Identifier: doi:10.1006/jabr.1994.1267
M. Van den Bergh, Existence theorems for dualizing complexes over noncommutative graded and filtered rings, J. Algebra 195 (1997), 662--679.
Mathematical Reviews (MathSciNet): MR1469646
Digital Object Identifier: doi:10.1006/jabr.1997.7052
------, Noncommutative crepant resolutions, The legacy of Niels Henrik Abel, pp. 749--770, Springer-Verlag, Berlin, 2004.
Mathematical Reviews (MathSciNet): MR2074480
Zentralblatt MATH: 1047.00019
------, Three dimensional flops and noncommutative rings, Duke Math. J. 122 (2004), 423--455.
Mathematical Reviews (MathSciNet): MR2057015
Digital Object Identifier: doi:10.1215/S0012-7094-04-12231-6
Project Euclid: euclid.dmj/1082665284
A. Yekutieli, Dualizing complexes over noncommutative graded algebras, J. Algebra 153 (1992), 41--84.
Mathematical Reviews (MathSciNet): MR1195406
Digital Object Identifier: doi:10.1016/0021-8693(92)90148-F
------, Dualizing complexes, Morita equivalence and the derived Picard group of a ring, J. London Math. Soc. (2) 60 (1999), 723--746.
Mathematical Reviews (MathSciNet): MR1753810
Digital Object Identifier: doi:10.1112/S0024610799008108
A. Yekutieli and J. J. Zhang, Rings with Auslander dualizing complexes, J. Algebra 213 (1999), 1--51.
Mathematical Reviews (MathSciNet): MR1674648
Digital Object Identifier: doi:10.1006/jabr.1998.7657
------, Residue complexes over noncommutative rings, J. Algebra 259 (2003), 451--493.
Mathematical Reviews (MathSciNet): MR1955528
Digital Object Identifier: doi:10.1016/S0021-8693(02)00579-3

2009 © The University of Michigan