Sur les automorphismes born\'es de corps munis d'op\'erateurs

TL;DR

This paper provides a new, characteristic-independent proof for characterizing bounded automorphisms of algebraically closed fields and extends the approach to fields with operators.

Contribution

It introduces a novel proof technique applicable across all characteristics and generalizes the characterization to fields with additional operators.

Findings

Alternative proof valid in all characteristics

Generalization to fields with operators

Characterization of bounded automorphisms

Abstract

We give an alternative proof, valid in all characteristics, of a result of Lascar characterising the bounded automorphisms of an algebraically closed field. We generalise this method to various fields equipped with operators.