Title: Etale homotopy and sums-of-squares formulas
Authors: Daniel Dugger, Daniel C. Isaksen
Authors' e-mail address: ddugger@math.uoregon.edu, isaksen@math.wayne.edu
AMS classification number: 55P60, 15A63

Abstract:

This paper uses a relative of BP-cohomology to prove a theorem in 
characteristic p algebra.  Specifically, we obtain some new necessary 
conditions for the existence of sums-of-squares formulas over fields of 
characteristic p > 2.  These conditions were previously known in 
characteristic zero by results of Davis.  Our proof uses a generalized 
etale cohomology theory called etale BP2.