Existentially closed fields with G-derivations

TL;DR

This paper proves the existence of model companions for theories of fields equipped with G-derivations from formal group actions, providing geometric axiomatizations for these models.

Contribution

It establishes the model companions for fields with G-derivations and offers geometric axiomatizations, advancing the understanding of such algebraic structures.

Findings

Existence of model companions for fields with G-derivations.

Geometric axiomatizations of these model companions.

Extension of model theory to fields with formal group actions.

Abstract

We prove that the theories of fields with Hasse-Schmidt derivations corresponding to actions of formal groups admit model companions. We also give geometric axiomatizations of these model companions.