Generalized Koszul resolutions

TL;DR

This paper generalizes Koszul resolutions to characterize modules over noetherian rings that admit such resolutions, linking them to pure weight two modules.

Contribution

It introduces a generalized notion of Koszul resolutions and characterizes modules that admit these resolutions over noetherian rings.

Findings

Modules with a two-dimensional generalized Koszul resolution are precisely pure weight two modules.

Provides a new characterization of modules admitting generalized Koszul resolutions.

Extends classical Koszul resolution theory to a broader class of modules.

Abstract

The main objective of this paper is to generalize a notion of Koszul resolutions and charcterizing modules which admits such a resolution. We turn out that for a noetherian ring $A$ and a coherent $A$ module $M$, $M$ has a two dimensional generalized Koszul resolution if and only if $M$ is a pure weight two module in the sense of \cite{HM09}.