Vol. 2, No. 2, 2017

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Chow groups of some generically twisted flag varieties

Nikita A. Karpenko

Vol. 2 (2017), No. 2, 341–356
Abstract

We classify the split simple affine algebraic groups G of types A and C over a field with the property that the Chow group of the quotient variety EP is torsion-free, where P G is a special parabolic subgroup (e.g., a Borel subgroup) and E is a generic G-torsor (over a field extension of the base field). Examples of G include the adjoint groups of type A. Examples of EP include the Severi–Brauer varieties of generic central simple algebras.

Keywords
central simple algebras, algebraic groups, projective homogeneous varieties, Chow groups
Mathematical Subject Classification 2010
Primary: 14C25, 20G15
Milestones
Received: 15 February 2016
Revised: 26 April 2016
Accepted: 11 May 2016
Published: 14 December 2016
Authors
Nikita A. Karpenko
Mathematical & Statistical Sciences
University of Alberta
632 Central Academic Building
Edmonton, AB T6G 2G1
Canada