TY - JOUR

T1 - TWISTED FORMS OF CLASSICAL GROUPS

AU - Voronetsky, E

N1 - Times Cited in Web of Science Core Collection: 1 Total Times Cited: 1 Cited Reference Count: 18

PY - 2023

Y1 - 2023

N2 - Twisted forms of classical reductive group schemes are described in a unified way. Such group schemes are constructed from algebraic objects of finite rank, excluding some exceptions of small rank. These objects, called the augmented odd form algebras, consist of 2-step nilpotent groups with an action of the underlying commutative ring, hence the basic descent theory for them will be developed. Finally, classical isotropic reductive groups are described as odd unitary groups up to an isogeny.

AB - Twisted forms of classical reductive group schemes are described in a unified way. Such group schemes are constructed from algebraic objects of finite rank, excluding some exceptions of small rank. These objects, called the augmented odd form algebras, consist of 2-step nilpotent groups with an action of the underlying commutative ring, hence the basic descent theory for them will be developed. Finally, classical isotropic reductive groups are described as odd unitary groups up to an isogeny.

KW - Classical groups

KW - unitary groups

U2 - 10.1090/spmj/1750

DO - 10.1090/spmj/1750

M3 - Article

VL - 34

SP - 179

EP - 204

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 2

ER -