Massey products in Galois cohomology and the Elementary Type Conjecture

Claudio Quadrelli

Published 2022-03-30Version 1

Let $p$ be a prime. We prove that a positive solution to Efrat's Elementary Type Conjecture implies a positive solution to a strengthened version of Minac-T\^an's Massey Vanishing Conjecture. Consequently, the maximal pro-$p$ Galois group of a field $K$ containing a root of 1 of order $p$ satisfies the strong $n$-Massey vanishing property in several relevant cases, e.g.: $K$ is a local field; $K$ is a PAC field; $K$ is a $p$-rigid field; $K$ is algebraic extension of a global field with finitely generated maximal pro-$p$ Galois group.