Abstract
We study Koszul homology over local Gorenstein rings. It is well known that if an ideal is strongly Cohen–Macaulay the Koszul homology algebra satisfies Poincaré duality. We prove a version of this duality which holds for all ideals and allows us to give two criteria for an ideal to be strongly Cohen–Macaulay. The first can be compared to a result of Hartshorne and Ogus; the second is a generalization of a result of Herzog, Simis, and Vasconcelos using sliding depth.
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Acknowledgments
The authors would like to thank Craig Huneke for useful conversations regarding this paper, including comments which simplified the proof of Theorem 2.2.
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This research was partly supported by NSF grant DMS 0901427 (J.S.), and NSF grant DMS 100334 (C.M.).
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Miller, C., Rahmati, H. & Striuli, J. Duality for Koszul homology over Gorenstein rings. Math. Z. 276, 329–343 (2014). https://doi.org/10.1007/s00209-013-1202-5
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DOI: https://doi.org/10.1007/s00209-013-1202-5