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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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$R$-equivalence in spinor groups
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by Vladimir Chernousov and Alexander Merkurjev PDF
J. Amer. Math. Soc. 14 (2001), 509-534 Request permission


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
  • MR Author ID: 199556
  • Email:
  • Alexander Merkurjev
  • Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095-1555
  • MR Author ID: 191878
  • ORCID: 0000-0002-4447-1838
  • Email:
  • 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.
  • © Copyright 2001 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 14 (2001), 509-534
  • MSC (2000): Primary 11E04, 20G15; Secondary 14C35
  • DOI:
  • MathSciNet review: 1824991