Geodesic
Reduction of structure to parabolic subgroups
Documenta mathematica, Tome 27 (2022), pp. 1421-1446 Cet article a éte moissonné depuis la source EMS Press

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Let G be an affine group over a field of characteristic not two. A G-torsor is called 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.
DOI : 10.4171/dm/901
Classification : 11E39, 11E72, 16W10, 20G07, 20G15
Mots-clés : Galois cohomology, algebraic geometry, rings and algebras 
@article{10_4171_dm_901,
     author = {Danny Ofek},
     title = {Reduction of structure to parabolic subgroups},
     journal = {Documenta mathematica},
     pages = {1421--1446},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/901},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/901/}
}
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Danny Ofek. Reduction of structure to parabolic subgroups. Documenta mathematica, Tome 27 (2022), pp. 1421-1446. doi: 10.4171/dm/901

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