Difference modules and difference cohomology

TL;DR

This paper explores the homological algebra of difference representations, introducing cohomology theories for difference-discrete and difference-rational cases, and establishing spectral sequences linking these to classical cohomology.

Contribution

It develops new cohomology theories for difference modules and demonstrates spectral sequences connecting them with standard cohomology theories.

Findings

Defined cohomology theories for difference-discrete and difference-rational modules.

Established spectral sequences relating difference cohomology to classical cohomology.

Provided foundational results in the homological algebra of difference representations.

Abstract

We give some basics about homological algebra of difference representations. We consider both the difference-discrete and the difference-rational case. We define the corresponding cohomology theories and show the existence of spectral sequences relating these cohomology theories with the standard ones.