The Hopf condition for bilinear forms over arbitrary fields, by Daniel Dugger and Daniel C. Isaksen

We settle an old question about the existence of certain "sums-of-squares" formulas over a field F. A classical result, due originally to Hopf and proven via topological methods, says that if such a formula exists over a field of characteristic 0 then certain binomial coefficients must be even. We use motivic methods to prove that the result also holds for fields of characteristic p.

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