Analogues of Morozov Theorem in characteristic p>0

TL;DR

This paper extends Morozov's theorem to reductive groups over fields of positive characteristic, characterizing certain subalgebras and enabling the construction of canonical parabolic subgroups in characteristic p>0.

Contribution

It provides an analogue of Morozov's theorem for characteristic p>0, under specific conditions, broadening the understanding of parabolic subalgebras in positive characteristic.

Findings

Established Morozov analogue for separably good characteristics

Characterized subalgebras of parabolic subgroups via nilradicals

Extended Atiyah-Bott construction to characteristic p>0

Abstract

Let G be a reductive group over an algebraically closed field of positive characteristic. In this article we show an analogue for Morozov theorem for characteristics that are separably good for G (and under additional hypotheses on the group). This theorem characterises, when p= 0, subalgebras of parabolic subgroups of G with respect to their nilradical. If now k is an arbitrary field, let C be a smooth projective and geometrically connected curve. Let G be a reductive C-group scheme, which is the twisted form of a constant C-group. The aforementioned analogue is in particular useful to extend the construction of the canonical parabolic subgroup of G proposed by M. Atiyah and R. Bott when k is of characteristic 0, to the characteristic p>0 framework.