DETECTING KOSZULNESS AND RELATED HOMOLOGICAL PROPERTIES FROM THE ALGEBRA STRUCTURE OF KOSZUL HOMOLOGY

DOI10.1017/nmj.2018.20zbMath1457.13036arXiv1611.04001OpenAlexW2962976336WikidataQ114655136 ScholiaQ114655136MaRDI QIDQ5112475

Gabriel Sosa, Peder Thompson, Roger Dellaca, Vivek Mukundan, Denise Rangel Tracy, Liana M. Şega, A. Cröll, Justin Hoffmeier, Anjan Kumar Gupta

Publication date: 29 May 2020

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.04001

zbMATH Keywords

Poincaré seriesKoszul homologyKoszul algebraTate resolutionYoneda algebraGolod rings

Mathematics Subject Classification ID

Syzygies, resolutions, complexes and commutative rings (13D02) Homological functors on modules of commutative rings (Tor, Ext, etc.) (13D07) Quadratic and Koszul algebras (16S37)

Related Items

Poincaré series of compressed local Artinian rings with odd top socle degree ⋮ Extremal growth of Betti numbers and trivial vanishing of (co)homology ⋮ A criterion for modules over Gorenstein local rings to have rational Poincaré series ⋮ A survey on the Koszul homology algebra

Uses Software

• Macaulay2

Cites Work

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• Homological properties of the homology algebra of the Koszul complex of a local ring: examples and questions
• Conditions for the Yoneda algebra of a local ring to be generated in low degrees
• Cohomology over fiber products of local rings
• Poincaré series of modules over local rings of small embedding codepth or small linking number
• Small homomorphisms of local rings
• Factoring out the socle of a Gorenstein ring
• Poincaré series of compressed local Artinian rings with odd top socle degree
• Bettireihen von Faserprodukten lokaler Ringe
• Subadditivity of syzygies of Koszul algebras
• Poincaré series of modules over compressed Gorenstein local rings
• Matric Massey products
• Koszul modules
• Linearity defects of modules over commutative rings
• Free resolutions over short local rings
• The Poincaré Series Of Stretched Cohen-Macaulay Rings
• Poincare Series of Modules Over Local Rings
• Edge ideals and DG algebra resolutions
• Homological properties of powers of the maximal ideal of a local ring