Model theory of fields with finite group scheme actions

Abstract

We study model theory of fields with actions of a fixed finite group scheme. We prove the existence and simplicity of a model companion of the theory of such actions, which generalizes our previous results about truncated iterative Hasse-Schmidt derivations and about Galois actions. As an application of our methods, we obtain a new model complete theory of actions of a finite group on fields of finite imperfection degree.