Free resolutions over short Gorenstein local rings

Abstract

Let R be a local ring with maximal ideal m admitting a non-zero element a\in\fm for which the ideal (0:a) is isomorphic to R/aR. We study minimal free resolutions of finitely generated R-modules M, with particular attention to the case when m^4=0. Let e denote the minimal number of generators of m. If R is Gorenstein with m^4=0 and e\ge 3, we show that \Poi MRt is rational with denominator \HH R{-t} =1-et+et^2-t^3, for each finitely generated R-module M. In particular, this conclusion applies to generic Gorenstein algebras of socle degree 3.

19 pages; new title, minor changes and extended bibliography

References in corpus (1)

• Free resolutions over short Gorenstein local rings

Cited by in corpus (10)

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• Burch ideals and Burch rings
• Short Koszul modules
• Asymptotic behaviors of representations of graded categories with inductive functors
• Gorensteinness of short local rings in terms of the vanishing of Ext and Tor
• Absolutely Koszul algebras and the Backelin-Roos property
• On the regularity and Koszulness of modules over local rings