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Subspaces of non-commutative spaces
Author(s):
S.
Paul
Smith
Journal:
Trans. Amer. Math. Soc.
354
(2002),
2131-2171.
MSC (2000):
Primary 14A22;
Secondary 18E15, 16S38, 16P40, 18F99
Posted:
February 14, 2002
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Abstract:
This paper concerns the closed points, closed subspaces, open subspaces, weakly closed and weakly open subspaces, and effective divisors, on a non-commutative space.
References:
-
- 1.
- M. Artin, J. Tate and M. Van den Bergh, Some algebras related to automorphisms of elliptic curves, in The Grothendieck Festschrift, Vol.1, 33-85, Birkhauser, Boston 1990. MR 92e:14002
- 2.
- M. Artin, J. Tate and M. Van den Bergh, Modules over regular algebras of dimension 3, Invent. Math., 106 (1991) 335-388. MR 93e:16055
- 3.
- M. Artin and J. Zhang, Non-commutative Projective Schemes, Adv. Math., 109 (1994), 228-287. MR 96a:14004
- 4.
- M.J. Asensio, M. Van den Bergh, and F. Van Oystaeyen, A new algebraic approach to microlocalization of filtered rings, Trans. Amer. Math. Soc., 316 (1989) 537-553. MR 90c:16001
- 5.
- G. Cauchon, Les T-anneaux, la condition (H) de Gabriel et ses conséquences, Comm. Alg., 4 (1976) 11-50. MR 52:13922
- 6.
- P. Gabriel, Des catégories abéliennes, Bull. Soc. Math. France 90 (1962), 323-448. MR 38:1144
- 7.
- K.R. Goodearl and R.B. Warfield, An Introduction to Noncommutative Noetherian Rings, Lond. Math. Soc. Texts, no. 16, Camb. Univ. Press, Cambridge, 1989. MR 91c:16001
- 8.
- A. Grothendieck (with P. Berthelot and L. Illusie), Théorie des intersections et Théorème de Riemann-Roch (SGA 6), Lecture Notes in Math. 225, Springer-Verlag, Berlin/New York, 1971. MR 50:7133
- 9.
- R. Hartshorne, Residues and Duality, Lecture Notes in Math. 20, Springer-Verlag, Berlin/New York, 1966. MR 36:5145
- 10.
- R. Hartshorne, Algebraic Geometry, Springer-Verlag, 1977. MR 57:3116
- 11.
- P. Jørgensen, Intersection theory on non-commutative surfaces, Trans. Amer. Math. Soc., 352 (2000) 5817-5854. MR 2001b:14005
- 12.
- P. Jørgensen and S.P. Smith, Curves on non-commutative surfaces, in preparation.
- 13.
- P. Jørgensen and S.P. Smith, Intersection theory for the blow-up of a non-commutative surface, in preparation.
- 14.
- A. Joyal and R. Street, An introduction to Tannaka duality and quantum groups, pp. 413-492 in Category Theory, Proceedings, Como 1990, Eds. A. Carboni, M.C. Pedicchio, G. Rosolini, Lect. Notes in Math., vol. 1488, Springer Verlag, 1991. MR 93f:18015
- 15.
- A. Kapustin, A. Kuznetzov, and D. Orlov, Noncommutative Instantons and Twistor Transform, Comm. Math. Phys. 221 (2001), 385-432.
- 16.
- L. Le Bruyn and M. Van den Bergh, On quantum spaces of Lie algebras, Proc. Amer. Math. Soc., 119 (1993) 407-414. MR 93k:17021
- 17.
- J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings, John Wiley and Sons, 1987. MR 89j:16023
- 18.
- C. Pappacena, The injective spectrum of a non-commutative space, manuscript, February 2001, QA 0108175.
- 19.
- N. Popescu, Abelian Categories with Applications to Rings and Modules, Academic Press (Lond. Math. Soc. Monographs), 1973. MR 49:5130
- 20.
- A.L. Rosenberg, Non-commutative algebraic geometry and representations of quantized algebras, Vol. 330, Kluwer Academic Publishers, 1995. MR 97b:14004
- 21.
- A.L. Rosenberg, Non-commutative schemes, Compos. Math., 112 (1998) 93-125. MR 99h:14002
- 22.
- S.P. Smith and J. Zhang, Curves on quasi-schemes, Algebras and Representation Theory, 1 (1998) 311-351. MR 2001a:16046
- 23.
- S.P. Smith, Integral non-commutative spaces, J. Algebra, to appear, QA 0104046.
- 24.
- S.P. Smith, Maps between non-commutative spaces, Preprint, University of Washington, 2000.
- 25.
- M. Van den Bergh, Blowing up on non-commutative smooth surfaces, Mem. Amer. Math. Soc., 154 (2001), No. 734.
- 26.
- M. Van Gastel and M. Van den Bergh, Graded modules of Gelfand-Kirillov dimension one over three-dimensional Artin-Schelter regular algebras, J. Algebra, 196 (1997), 697-707. MR 99c:16020
- 27.
- A.B. Verevkin, On a non-commutative analogue of the category of coherent sheaves on a projective scheme, Amer. Math. Soc. Transl. (2) 151 (1992) 41-53. MR 93j:14002
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Additional Information:
S.
Paul
Smith
Affiliation:
Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98195
Email:
smith@math.washington.edu
DOI:
10.1090/S0002-9947-02-02963-X
PII:
S 0002-9947(02)02963-X
Received by editor(s):
November 28, 2000
Received by editor(s) in revised form:
April 5, 2001 and September 20, 2001
Posted:
February 14, 2002
Additional Notes:
The author was supported by NSF grant DMS-0070560
Copyright of article:
Copyright
2002,
American Mathematical Society
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