Relative versions of theorems of Bogomolov and Sukhanov over perfect fields

Abstract

In this paper, we investigate some aspects of representation theory of reductive groups over non-algebraically closed fields. Namely, we state and prove relative versions of well-known theorems of Bogomolov and of Sukhanov, which are related to observable and quasi-parabolic subgroups of linear algebraic groups over non-algebraically closed perfect fields.