Vol. 16, No. 1, 2022

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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
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.

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