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Pfister's local–global principle and systems of quadratic forms

Pfister's local–global principle and systems of quadratic forms Let q be a unimodular quadratic form over a field K. Pfister's famous local–global principle asserts that q represents a torsion class in the Witt group of K if and only if it has signature 0, and that in this case, the order of Witt class of q is a power of 2. We give two analogues of this result to systems of quadratic forms, the second of which applying only to nonsingular pairs. We also prove a counterpart of Pfister's theorem for finite‐dimensional K‐algebras with involution, generalizing a result of Lewis and Unger. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Pfister's local–global principle and systems of quadratic forms

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References (23)

Publisher
Wiley
Copyright
© 2020 London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms.12385
Publisher site
See Article on Publisher Site

Abstract

Let q be a unimodular quadratic form over a field K. Pfister's famous local–global principle asserts that q represents a torsion class in the Witt group of K if and only if it has signature 0, and that in this case, the order of Witt class of q is a power of 2. We give two analogues of this result to systems of quadratic forms, the second of which applying only to nonsingular pairs. We also prove a counterpart of Pfister's theorem for finite‐dimensional K‐algebras with involution, generalizing a result of Lewis and Unger.

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Dec 1, 2020

Keywords: ;

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