Geodesic
Reduction of structure to parabolic subgroups
Documenta mathematica, Tome 27 (2022), pp. 1421-1446.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Let $G$ be an affine group over a field of characteristic not two. A $G$-torsor is called \textit{isotropic} if it admits reduction of structure to a proper parabolic subgroup of $G$. This definition generalizes isotropy of affine groups and involutions of central simple algebras. When does $G$ admit anisotropic torsors? Building on work of J. Tits, we answer this question for simple groups. We also give an answer for connected and semisimple $G$ under certain restrictions on its root system.
Classification : 11E72, 20G15, 20G07, 11E39, 16W10
Keywords: linear algebraic groups, parabolic subgroups, isotropy, anisotropy, torsors, Galois cohomology 
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     author = {Ofek, Danny},
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Ofek, Danny. Reduction of structure to parabolic subgroups. Documenta mathematica, Tome 27 (2022), pp. 1421-1446. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a30/