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$R$-equivalence in spinor groups


Authors: Vladimir Chernousov and Alexander Merkurjev
Journal: J. Amer. Math. Soc. 14 (2001), 509-534
MSC (2000): Primary 11E04, 20G15; Secondary 14C35
DOI: https://doi.org/10.1090/S0894-0347-01-00365-4
Published electronically: February 27, 2001
MathSciNet review: 1824991
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Abstract:

The groups of $R$-equivalent classes of the spinor groups of non-degenerate quadratic forms over arbitrary fields are computed in terms of certain $K$-cohomology groups of corresponding quadric hypersurfaces. As an application, examples of non-rational spinor groups of every dimension $\geq 6$are given.


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Additional Information

Vladimir Chernousov
Affiliation: Fakultät Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
Email: chernous@mathematik.uni-bielefeld.de

Alexander Merkurjev
Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095-1555
Email: merkurev@math.ucla.edu

DOI: https://doi.org/10.1090/S0894-0347-01-00365-4
Received by editor(s): January 5, 2000
Received by editor(s) in revised form: June 5, 2000
Published electronically: February 27, 2001
Additional Notes: The first author gratefully acknowledges the support of SFB 343 “Diskrete Strukturen in der Mathematik", TMR ERB FMRX CT-97-0107 and the hospitality of the University of Bielefeld.
The second author was partially supported by NSF Grant DMS 9801646.
Article copyright: © Copyright 2001 American Mathematical Society

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