Serre duality for noncommutative projective schemes

Yekutieli, Amnon; Zhang, James

doi:10.1090/S0002-9939-97-03782-9

Serre duality for noncommutative projective schemes
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by Amnon Yekutieli and James J. Zhang

Proc. Amer. Math. Soc. 125 (1997), 697-707

DOI: https://doi.org/10.1090/S0002-9939-97-03782-9

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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

M. Artin and J. J. Zhang, Noncommutative projective schemes, Adv. Math. 109 (1994), no. 2, 228–287. MR 1304753, DOI 10.1006/aima.1994.1087
Robin Hartshorne, Residues and duality, Lecture Notes in Mathematics, No. 20, Springer-Verlag, Berlin-New York, 1966. Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64; With an appendix by P. Deligne. MR 0222093, DOI 10.1007/BFb0080482
Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157, DOI 10.1007/978-1-4757-3849-0
P. Jørgensen, Serre-Duality for $\mathrm {Tails}(A)$, Proc. Amer. Math. Soc., this issue.
Joseph J. Rotman, An introduction to homological algebra, Pure and Applied Mathematics, vol. 85, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1979. MR 538169
Amnon Yekutieli, Dualizing complexes over noncommutative graded algebras, J. Algebra 153 (1992), no. 1, 41–84. MR 1195406, DOI 10.1016/0021-8693(92)90148-F