Triple Massey products and absolute Galois groups

Abstract

Let $p$ be a prime number, $F$ a field containing a root of unity of order $p$, and $G_F$ the absolute Galois group. Extending results of Hopkins, Wickelgren, Minac and Tan, we prove that the triple Massey product $H^1(G_F{)}^3\to H^2(G_F)$ contains $0$ whenever it is nonempty. This gives a new restriction on the possible profinite group structure of $G_F$.

A first version of this paper, by the second-named author, was earlier posted as arXiv:1411.4146. The current version gives a purely group-cohomological proof of the main result. To appear in the Journal of the European Mathematical Society

Cited by in corpus (2)

• Triple Massey products vanish over all fields
• Counting Galois ${\mathbb{U}}_4({\mathbb{F}}_p)$-extensions using Massey products