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.

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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