Vol. 4, No. 2, 2019

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

Nikita Karpenko and Eoin Mackall

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 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 EB to the graded ring associated with the coniveau filtration of the Grothendieck ring of EB 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
Received: 28 June 2018
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