Complete reducibility and isogenies over an arbitrary field

TL;DR

This paper explores how the property of G-complete reducibility is affected by isogenies over any field, providing insights into the structural behavior of algebraic groups.

Contribution

It offers a new analysis of G-complete reducibility's behavior under isogenies over arbitrary fields, extending previous results beyond algebraically closed fields.

Findings

G-complete reducibility is preserved under certain isogenies

Characterization of G-complete reducibility over arbitrary fields

Extension of known results to more general field settings

Abstract

In this paper, we investigate how the property of $G$-complete reducibility behaves under isogenies over an arbitrary field.