The Hopf condition for bilinear forms over arbitrary fields


We settle an old question about the existence of certain ‘sums-of-squares’ formulas over a field $F$, 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 vanish. We prove that this result also holds over fields of characteristic $p>2$.


Daniel Dugger

Department of Mathematics, University of Oregon, Eugene, OR 97403, United States

Daniel C. Isaksen

Department of Mathematics, Wayne State University, Detroit, MI 48202, United States