Vanishing of Massey products and Brauer groups

TL;DR

This paper explores the relationship between the vanishing of Massey products in Galois cohomology and classical Brauer group results, providing new insights especially for global fields.

Contribution

It establishes a connection between recent cohomological results and classical algebraic structures, extending vanishing properties to global fields.

Findings

Vanishing of triple Massey products relates to Brauer group properties.

Stronger vanishing results are proven for global fields.

Links between Galois cohomology and central simple algebras are clarified.

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.