Massey products in Galois cohomology and the Elementary Type Conjecture

Abstract

Let $p$ be a prime. We prove that a positive solution to Efrat's Elementary Type Conjecture implies a positive solution to the strengthened version of Minač--Tân's Massey Vanishing Conjecture in the case of finitely generated maximal pro-$p$ Galois groups whose pro-$p$ cyclotomic character has torsion-free image. Consequently, the maximal pro-$p$ Galois group of a field $\mathbb{K}$ containing a root of 1 of order $p$ (and also \sqrt{-1} if $p=2$) satisfies the strong $n$-Massey vanishing property for every $n>2$ (which is equivalent to the cup-defining $n$-Massey product property for every $n>2$, as defined by Minač--Tân) in several relevant cases.

arXiv commentFinal version, published on the Journal of Number Theory, 258 (2024), 40-65

References in corpus (8)

• Triple Massey products vanish over all fields
• The Kummerian Property and Maximal Pro-$p$ Galois Groups
• Bloch-Kato pro-p groups and locally powerful groups
• The Massey vanishing conjecture for number fields
• Koszul algebras and quadratic duals in Galois cohomology
• Four-fold Massey products in Galois cohomology
• Groups of p-absolute Galois type that are not absolute Galois groups
• Oriented pro-$\ell$ groups with the Bogomolov-Positselski property

Cited by in corpus (1)

• Chasing maximal pro-p Galois groups via 1-cyclotomicity