On the Massey vanishing conjecture and formal Hilbert 90

Abstract Let be a prime number, let be a profinite group, let be a continuous character, and for all write for the twist of by the ‐action. Suppose that satisfies a formal version of Hilbert's Theorem 90: for all open subgroups and every , the map is surjective. We show that the Massey Vanishing Conjecture for triple Massey products and some degenerate fourfold Massey products holds for . A key step in our proof is the construction of a Hilbert 90 module for : a discrete ‐module that plays the role of the Galois module for the absolute Galois group of a field of characteristic different from .