The Massey Vanishing Conjecture for fourfold Massey products modulo 2

TL;DR

This paper proves the Massey Vanishing Conjecture for fourfold Massey products modulo 2, establishing that such products, when defined over any field, always vanish, thus advancing understanding in algebraic cohomology.

Contribution

It provides a proof of the Massey Vanishing Conjecture specifically for fourfold Massey products modulo 2, a case previously unresolved.

Findings

Fourfold Massey products modulo 2 always vanish when defined over any field.

The proof confirms the conjecture for all fields, not just specific cases.

Advances the understanding of Massey products in algebraic cohomology.

Abstract

We prove the Massey Vanishing Conjecture for $n=4$ and $p=2$. That is, we show that for all fields $F$, if a fourfold Massey product modulo $2$ is defined over $F$, then it vanishes over $F$.