Duality for Koszul Homology over Gorenstein Rings
Claudia Miller, Hamidreza Rahmati, Janet Striuli
TL;DR
This paper explores the duality properties of Koszul homology over Gorenstein rings, establishing new criteria for an ideal to be strongly Cohen-Macaulay and extending existing duality results.
Contribution
It generalizes Poincaré duality for Koszul homology to all ideals over Gorenstein rings and introduces two novel criteria for strong Cohen-Macaulayness.
Findings
Koszul homology algebra satisfies Poincaré duality for strongly Cohen-Macaulay ideals.
A new duality version applicable to all ideals over Gorenstein rings.
Two criteria for identifying strongly Cohen-Macaulay ideals, extending previous results.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology