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.
- Gorenstein ring
- Poincaré duality
- Strongly Cohen-Macaulay ideals
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