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Sur les sous-groupes paraboliques associés à un groupe réductif

Abstract : Let k be an algebraically closed field of characteristic 0 and G be a (connected) reductive k-group, we denote by Lie(G) its Lie algebra. Assume Lie(G) to be semisimple. A theorem of Morozov leads to a characterisation of the parabolic subalgebras of g in terms of nilpotent elements of their solvable radical. In this article we aim to obtain analogues of Morozov's theorem in characteristic p>0. This requires to find the good counterparts in characteristic p>0 of objects and notions classically related to the characteristic 0 framework, such as exponentiation. The generalisation of results first obtained by P. Deligne and V. Balaji, P. Deligne and A. J. Parameswaran we propose to show in this article leads to the desired analogue under some conditions on p and G. It also provides an additional characterisation of the obtained parabolic subalgebra in terms of geometric invariant theory.
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https://hal.archives-ouvertes.fr/hal-02903773
Contributor : Marion Jeannin <>
Submitted on : Saturday, October 24, 2020 - 7:22:25 PM
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  • HAL Id : hal-02903773, version 2

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Marion Jeannin. Sur les sous-groupes paraboliques associés à un groupe réductif. Mathématiques [math]. Université de Lyon (COMUE), 2020. Français. ⟨hal-02903773v2⟩

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