### 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.

Daniel Dugger <ddugger@math.uoregon.edu>
Daniel C. Isaksen <isaksen@math.wayne.edu>