Torsors for Difference Algebraic Groups
Annette Bachmayr, Michael Wibmer

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.
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