Free resolutions over short local rings

2007/07/30 by Luchezar L. Avramov, Srikanth B. Iyengar, Avramov, Luchezar L. +3 · 2 citations
Mathematics · #13D02 (Primary) #13D07 (Secondary) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13D02 #msc:13D07

paper · pdf · doi:10.48550/arxiv.0707.4451

17 pages; number of minor changes. This article will appear in the Journal of the London Math. Soc

arxiv created 2008/04/09 · arxiv updated 2009/12/01

Abstract

The structure of minimal free resolutions of finite modules M over commutative local rings (R,m,k) with m³=0 and rank_k(m²) < rank_k(m/m²)is studied. It is proved that over generic R every M has a Koszul syzygy module. Explicit families of Koszul modules are identified. When R is Gorenstein the non-Koszul modules are classified. Structure theorems are established for the graded k-algebra Ext_R(k,k) and its graded module Ext_R(M,k).

Cited by

• Claus Michael Ringel's main contributions to Gorenstein-projective modules
• Koszul property and finite linearity defect over g-stretched local rings

Related

• Minimal free resolution of a finitely generated module over a regular local ring
• Free resolutions over commutative Koszul algebras
• DG module structures and minimal free resolutions modulo an exact zero-divisor
• On a minimal free resolution of the residue field over a local ring of codepth 3 of class T
• Asymmetric complete resolutions and vanishing of Ext over Gorenstein rings