Triple Massey products vanish over all fields

TL;DR

This paper proves that all absolute Galois groups of fields have vanishing triple Massey products, revealing new structural properties and extending results to higher Massey products.

Contribution

It establishes the universal vanishing of triple Massey products over all fields' absolute Galois groups, a significant advancement in Galois cohomology.

Findings

Triple Massey products vanish over all fields' absolute Galois groups

Corollaries for the structure of maximal pro-p Galois groups

Vanishing results for some higher Massey products

Abstract

We show that the absolute Galois group of any field has the vanishing triple Massey product property. Several corollaries for the structure of maximal pro-$p$-quotient of absolute Galois groups are deduced. Furthermore, the vanishing of some higher Massey products is proved.