#### Vol. 4, No. 2, 2019

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On the K-theory coniveau epimorphism for products of Severi–Brauer varieties

### Appendix: Eoin Mackall

Vol. 4 (2019), No. 2, 317–344
##### Abstract

For $X$ a product of Severi–Brauer varieties, we conjecture that if the Chow ring of $X$ is generated by Chern classes, then the canonical epimorphism from the Chow ring of $X$ to the graded ring associated to the coniveau filtration of the Grothendieck ring of $X$ is an isomorphism. We show this conjecture is equivalent to the condition that if $G$ is a split semisimple algebraic group of type $\mathit{AC}$, $B$  is a Borel subgroup of $G$ and $E$ is a standard generic $G$-torsor, then the canonical epimorphism from the Chow ring of $E∕B$ to the graded ring associated with the coniveau filtration of the Grothendieck ring of $E∕B$ is an isomorphism. In certain cases we verify this conjecture.

##### Keywords
algebraic groups, projective homogeneous varieties, Chow groups
##### Mathematical Subject Classification 2010
Primary: 14C25, 20G15
##### Milestones
Revised: 19 October 2018
Accepted: 6 November 2018
Published: 16 June 2019
##### Authors
 Nikita Karpenko Department of Mathematical & Statistical Sciences University of Alberta Edmonton, AB Canada Eoin Mackall Department of Mathematical & Statistical Sciences University of Alberta Edmonton, AB Canada Eoin Mackall Department of Mathematical & Statistical Sciences University of Alberta Edmonton, AB Canada