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arXiv · 0707.4451

Free resolutions over short local rings

Luchezar L. Avramov·Srikanth B. Iyengar·Liana M. Sega
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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).

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BibTeXRIS

Luchezar L. Avramov, Srikanth B. Iyengar, Liana M. Sega. 2008-04-09. Free resolutions over short local rings. https://arxiv.org/abs/0707.4451

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