Vanishing of Massey products and Brauer groups

Abstract

Let p be a prime number and F a field containing a root of unity of order p. We relate recent results on vanishing of triple Massey products in the mod-p Galois cohomology of F, due to Hopkins, Wickelgren, Minac, and Tan, to classical results in the theory of central simple algebras. For global fields, we prove a stronger form of the vanishing property.