Differential Modules with Complete Intersection Homology

TL;DR

This paper explores differential modules with complete intersection homology, comparing them to Koszul complexes, and constructs a generalized Koszul differential module to extend classical properties.

Contribution

It introduces a new class of differential modules with complete intersection homology and constructs a generalized Koszul differential module.

Findings

Construction of a Koszul differential module generalizing the classical Koszul complex

Comparison of properties between differential modules and Koszul complexes

Analysis of which classical properties extend to the new setting

Abstract

Differential modules are natural generalizations of complexes. In this paper, we study differential modules with complete intersection homology, comparing and contrasting the theory of these differential modules with that of the Koszul complex. We construct a Koszul differential module that directly generalizes the classical Koszul complex and investigate which properties of the Koszul complex can be generalized to this setting.