The Hopf condition for bilinear forms over arbitary fields

Abstract: We settle an old question about the existence of certain `sums-of-squares' formulas over a field F. This is related to the composition problem 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 show that the same result holds over characteristic p fields.

• Dvi file . Preprint, 2003.