English

The Hopf condition for bilinear forms over arbitrary fields

Rings and Algebras 2007-05-23 v1 Algebraic Geometry Algebraic Topology

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.

Keywords

Cite

@article{arxiv.math/0309197,
  title  = {The Hopf condition for bilinear forms over arbitrary fields},
  author = {Daniel Dugger and Daniel C. Isaksen},
  journal= {arXiv preprint arXiv:math/0309197},
  year   = {2007}
}