Analogues of Morozov Theorem in 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.

arXiv comment39 pages, in English. v2->v3: mistakes in section 7 have been corrected, corollary 6.5 that classifies maximal proper p-subalgebras of the Lie algebra of a reductive group has been added