A self-dual complete resolution

TL;DR

This paper constructs a self-dual complete resolution for modules defined by embedded complete intersection ideals, leveraging Koszul homology and a gluing technique, leading to new isomorphisms between stable homology and cohomology.

Contribution

It introduces a novel self-dual complete resolution construction for modules over local rings with embedded complete intersections, expanding understanding of their homological properties.

Findings

Constructed a self-dual complete resolution for embedded complete intersection modules

Established an isomorphism between stable homology and cohomology modules

Utilized Koszul homology and a gluing construction in the process

Abstract

We construct a self-dual complete resolution of a module defined by a pair of embedded complete intersection ideals in a local ring. Our construction is based on a gluing construction of Herzog and Martsinkovsky and exploits the structure of Koszul homology in the embedded complete intersection case. As a consequence of our construction, we produce an isomorphism between certain stable homology and cohomology modules.