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Serre duality for noncommutative projective schemes

Author(s): Amnon Yekutieli; James J. Zhang
Journal: Proc. Amer. Math. Soc. 125 (1997), 697-707.
MSC (1991): Primary 14A22, 16W50, 16E30
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Abstract: We prove the Serre duality theorem for the noncommutative projective scheme $\;{\operatorname {proj }}\;A$ when $A$ is a graded noetherian PI ring or a graded noetherian AS-Gorenstein ring.

References:

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M. Artin and J. J. Zhang, Noncommutative projective schemes, Adv. in Math. 109 (1994), 228-287. MR 96a:14004

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R. Hartshorne, Residues and Duality, Lecture Notes in Math. 20, Springer-Verlag, Berlin, 1966. MR 36:5145

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R. Hartshorne, Algebraic Geometry, Springer-Verlag, New York, 1977. MR 57:3116

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P. Jørgensen, Serre-Duality for $\mathrm {Tails}(A)$, Proc. Amer. Math. Soc., this issue.

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J. J. Rotman, An Introduction to Homological Algebra, Academic Press, New York, 1979. MR 80k:18001

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A. Yekutieli, Dualizing complexes over noncommutative graded algebras, J. Alg. 153 (1992), 41-84. MR 94a:16077

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Additional Information:

Amnon Yekutieli
Affiliation: Department of Theoretical Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel
Email: amnon@wisdom.weizmann.ac.il

James J. Zhang
Affiliation: Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98195
Email: zhang@math.washington.edu

DOI: 10.1090/S0002-9939-97-03782-9
PII: S 0002-9939(97)03782-9
Keywords: noncommutative projective scheme, Serre duality theorem, Watts' theorem, dualizing sheaf, balanced dualizing complex
Received by editor(s): September 20, 1995
Received by editor(s) in revised form: January 24, 1996
Additional Notes: The first author is supported by an Allon Fellowship and is incumbent of the Anna and Maurice Boukstein Career Development Chair. The second author is supported by the NSF
Communicated by: Ken Goodearl
Copyright of article: Copyright 1997, American Mathematical Society

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