Twisted forms of classical groups
Group Theory
2026-05-08 v4 Representation Theory
Abstract
We give a unified description of twisted forms of classical reductive groups schemes. Such group schemes are constructed from algebraic objects of finite rank, excluding some exceptions of small rank. These objects, augmented odd form algebras, consist of -step nilpotent groups with an action of the underlying commutative ring, hence we develop basic descent theory for them. In addition, we describe classical isotropic reductive groups as odd unitary groups up to an isogeny.
Cite
@article{arxiv.2004.08627,
title = {Twisted forms of classical groups},
author = {Egor Voronetsky},
journal= {arXiv preprint arXiv:2004.08627},
year = {2026}
}
Comments
We added a description of classical isotropic reductive groups via odd form algebras