2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/116469This 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.Algebraic Topology55P60, 15A63text