Free resolutions over short local rings
Abstract
The structure of minimal free resolutions of finite modules M over commutative local rings (R,m,k) with m3=0 and rankk(m2) < rankk(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 ExtR(k,k) and its graded module ExtR(M,k).
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