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Journal of the London Mathematical Society Advance Access published online on April 2, 2008
Journal of the London Mathematical Society, doi:10.1112/jlms/jdn011
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© 2008 London Mathematical Society

Unramified elements in cycle modules

Alexander Merkurjev

Department of Mathematics
University of California
Los Angeles, CA 90095-1555
USA

Let X be an algebraic variety over a field F. We study the functor taking a cycle module M over F to the group of unramified elements M(F(X))nr of M(F(X)). We prove that this functor is represented by a cycle module. The existence of pull-back maps on M(F(X))nr for rational maps (under a mild condition) is established. An application to the R-equivalence on classifying varieties of algebraic groups is given.

2000 Mathematics Subject Classification 14F43, 14C25, 14E05 (primary).

The work has been supported by the NSF grant DMS #0652316.

Received May 29, 2007; revised December 6, 2007;
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