The Chow ring of the classifying space of the unitary group

Karpenko, Nikita A.; Merkurjev, Alexander S.

doi:10.2140/ant.2022.16.139

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The Chow ring of the classifying space of the unitary group

Nikita A. Karpenko and Alexander S. Merkurjev

Vol. 16 (2022), No. 1, 139–154

DOI: 10.2140/ant.2022.16.139

Abstract

We fill a gap in the literature by computing the Chow ring of the classifying space of the unitary group of a hermitian form on a finite-dimensional vector space over a separable quadratic field extension.

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Keywords

algebraic groups, unitary groups, torsors, hermitian forms, classifying spaces, Chow groups

Mathematical Subject Classification

Primary: 14C25, 20G15

Milestones

Received: 5 October 2020

Revised: 12 February 2021

Accepted: 19 April 2021

Published: 22 February 2022

Authors

Nikita A. Karpenko
Mathematical & Statistical Sciences University of Alberta Edmonton Canada

Alexander S. Merkurjev
Department of Mathematics University of California Los Angeles, CA United States

Vol. 16, No. 1, 2022