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A variant of a theorem by Springer
Authors:
I. Panin and U. Rehmann
Original publication:
Algebra i Analiz, tom 19 (2007), nomer 6.
Journal:
St. Petersburg Math. J. 19 (2008), 953-959
MSC (2000):
Primary 53A04; Secondary 52A40, 52A10
Posted:
August 21, 2008
MathSciNet review:
2411641
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Additional Information
Abstract: The theorem in question gives a sufficient condition for a quadratic space over a local ring  to contain a hyperbolic plane over  .
- [La]
T.
Y. Lam, The algebraic theory of quadratic forms, W. A.
Benjamin, Inc., Reading, Mass., 1973. Mathematics Lecture Note Series. MR 0396410
(53 #277)
- [P]
I. Panin, Rationally isotropic quadratic spaces are locally isotropic, www.math.uiuc.edu/K-theory/ 0671/2003
- [La]
- T. Y. Lam, The algebraic theory of quadratic forms, Math. Lecture Note Ser., W. A. Benjamin, Inc., Reading, MA, 1973. MR 0396410 (53:277)
- [P]
- I. Panin, Rationally isotropic quadratic spaces are locally isotropic, www.math.uiuc.edu/K-theory/ 0671/2003
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Additional Information
I. Panin
Affiliation:
St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
Address at time of publication:
SFB-701 at Fakultät für Mathematik, Universität Bielefeld, Germany
Email:
panin@pdmi.ras.ru, panin@math.uni-bielefeld.de
U. Rehmann
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
Email:
rehmann@math.uni-bielefeld.de
DOI:
http://dx.doi.org/10.1090/S1061-0022-08-01029-7
PII:
S 1061-0022(08)01029-7
Keywords:
Quadratic forms,
Springer's theorem,
local domain
Received by editor(s):
July 30, 2007
Posted:
August 21, 2008
Additional Notes:
This work is a part of the project SFB-701 at Fakultät für Mathematik, Universität Bielefeld. The first author is also supported by the Presidium of RAS Program “Fundamental Research”, an RFBR-grant, and the INTAS-05-1000008-8118 grant
Dedicated:
To the memory of D. K. Faddeev
Article copyright:
© Copyright 2008 American Mathematical Society
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