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The Hopf condition for bilinear forms over arbitrary fields

Daniel Dugger·Daniel C. Isaksen
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Abstract

We settle an old question about the existence of certain "sums-of-squares" formulas over a field F (which are the simplest examples of composition formulas for quadratic forms). A classical theorem says that if such a formula exists over a field of characteristic 0, then certain binomial coefficients must be even. We use motivic cohomology to prove that the same result holds in characteristic p.

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Daniel Dugger, Daniel C. Isaksen. 2003-09-11. The Hopf condition for bilinear forms over arbitrary fields. https://arxiv.org/abs/math/0309197

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