Abstract
It is shown that, over a field of characteristic not 2, the dimension of an anisotropic quadratic Pfister form of trivial total signature is at most twice the dimension of some central division algebra of exponent 2. The proof is based on computations with quadratic trace forms of central simple algebras.
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Acknowledgements
The author wishes to thank the referee for critical and very constructive comments, which helped to improve the presentation. Further thanks for comments and suggestions are due to Saurabh Gosavi, Bruno Kahn and Jean-Pierre Tignol.
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To the memory of David W. Lewis (1944–2021).
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