3-fold Massey products in Galois cohomology -- The non-prime case

Abstract: For $m\geq2$, let $F$ be a field of characteristic prime to $m$ and containing the roots of unity of order $m$, and let $G_F$ be its absolute Galois group. We show that the 3-fold Massey products $\langle\chi_1,\chi_2,\chi_3\rangle$, with $\chi_1,\chi_2,\chi_3\in H^1(G_F,\mathbb{Z}/m)$ and $\chi_1,\chi_3$ $\mathbb{Z}/m$-linearly independent, are non-essential. This was earlier proved for $m$ prime. Our proof is based on the study of unitriangular representations of $G_F$.