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 -equivalence in spinor groups
Author(s):
Vladimir
Chernousov;
Alexander
Merkurjev
Journal:
J. Amer. Math. Soc.
14
(2001),
509-534.
MSC (2000):
Primary 11E04, 20G15;
Secondary 14C35
Posted:
February 27, 2001
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Abstract:
The groups of  -equivalent classes of the spinor groups of non-degenerate quadratic forms over arbitrary fields are computed in terms of certain  -cohomology groups of corresponding quadric hypersurfaces. As an application, examples of non-rational spinor groups of every dimension  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:
10.1090/S0894-0347-01-00365-4
PII:
S 0894-0347(01)00365-4
Received by editor(s):
January 5, 2000
Received by editor(s) in revised form:
June 5, 2000
Posted:
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.
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Copyright
2001,
American Mathematical Society
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