Duality for Koszul Homology over Gorenstein Rings
Commutative Algebra
2011-12-15 v1
Abstract
We study Koszul homology over Gorenstein rings. If an ideal is strongly Cohen-Macaulay, the Koszul homology algebra satisfies Poincar\'e 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.
Cite
@article{arxiv.1112.3064,
title = {Duality for Koszul Homology over Gorenstein Rings},
author = {Claudia Miller and Hamidreza Rahmati and Janet Striuli},
journal= {arXiv preprint arXiv:1112.3064},
year = {2011}
}