Free resolutions over short local rings
Commutative Algebra
2008-04-09 v2
Abstract
The structure of minimal free resolutions of finite modules M over commutative local rings (R,m,k) with m^3=0 and rank_k(m^2) < rank_k(m/m^2)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).
Cite
@article{arxiv.0707.4451,
title = {Free resolutions over short local rings},
author = {Luchezar L. Avramov and Srikanth B. Iyengar and Liana M. Sega},
journal= {arXiv preprint arXiv:0707.4451},
year = {2008}
}
Comments
17 pages; number of minor changes. This article will appear in the Journal of the London Math. Soc