Free resolutions over short local rings

Details Free resolutions over short local rings Free resolutions over short local rings

2007-07-30

arxiv.org/abs/0707.4451v2

Mathematics

Commutative Algebra

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

Scientific paper

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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