2011/12/13 by Miller, Claudia, Rahmati, Hamidreza, Striuli, Janet · 1 citation
#13D02 #13D03 (Primary) 18G40 (Secondary) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1112.3064
We study Koszul homology over Gorenstein rings. 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.