## Annals of K-Theory

### Chow groups of some generically twisted flag varieties

Nikita Karpenko

#### 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 $E∕P$ 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 $E∕P$ include the Severi–Brauer varieties of generic central simple algebras.

#### Article information

Source
Ann. K-Theory, Volume 2, Number 2 (2017), 341-356.

Dates
Revised: 26 April 2016
Accepted: 11 May 2016
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.akt/1510841646

Digital Object Identifier
doi:10.2140/akt.2017.2.341

Mathematical Reviews number (MathSciNet)
MR3590349

Zentralblatt MATH identifier
1362.14006

#### Citation

Karpenko, Nikita. Chow groups of some generically twisted flag varieties. Ann. K-Theory 2 (2017), no. 2, 341--356. doi:10.2140/akt.2017.2.341. https://projecteuclid.org/euclid.akt/1510841646

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