Reduction of Structure to Parabolic Subgroups
Group Theory
2022-03-28 v2 Algebraic Geometry
Rings and Algebras
Abstract
Let be an affine group over a field of characteristic not two. A -torsor is called isotropic if it admits reduction of structure to a proper parabolic subgroup of . This definition generalizes isotropy of affine groups and involutions of central simple algebras. When does 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 under certain restrictions on its root system.
Cite
@article{arxiv.2203.03848,
title = {Reduction of Structure to Parabolic Subgroups},
author = {Danny Ofek},
journal= {arXiv preprint arXiv:2203.03848},
year = {2022}
}
Comments
22 pages; A typo in the statement of Theorem 1.3 and a typo in the paragraph preceding Lemma 5.3 are corrected