Torsors for Difference Algebraic Groups

TL;DR

This paper develops a cohomology framework for difference algebraic groups, enabling classification of torsors and advancing the Galois theory of differential equations with discrete parameters.

Contribution

It introduces a cohomology set for difference algebraic groups and applies it to classify torsors and study Galois theory in difference algebraic geometry.

Findings

Classifies torsors for large classes of difference algebraic groups

Provides tools for difference algebraic geometry

Applies to Galois theory of differential equations with discrete parameters

Abstract

We introduce a cohomology set for groups defined by algebraic difference equations and show that it classifies torsors under the group action. This allows us to compute all torsors for large classes of groups. We also develop some tools for difference algebraic geometry and present an application to the Galois theory of differential equations depending on a discrete parameter.