General n-Massey vanishing for all fields

Prove that every field satisfies n-Massey vanishing with respect to every prime p: all n-fold Massey products of elements of H^1(G_F, F_p) vanish whenever they are defined.

Background

The paper places its study of weak and genuine A_n-formality in the context of Massey products in Galois cohomology. Mináč and Tân conjectured that the vanishing phenomenon known for triple Massey products extends to arbitrary higher Massey products over every field and for every prime.

The paper notes that triple Massey vanishing is known for all fields and primes, and that several further cases of the conjecture have been established, including fourfold Massey vanishing at p=2. The cited conjecture nevertheless remains an explicitly stated general conjectural assertion in the introduction.

References

While Positselski showed that $(G_F,F_2)$ is not formal in general for local fields, Mináč and Tân conjectured in Conjecture 1.6 that the computation of Hopkins--Wickelgren generalises and all fields satisfy $n$-Massey vanishing with respect to $p$, i.e., all $n$-fold Massey products of elements in $H1(G_F,F_p)$ vanish whenever they are defined.

— Weak and genuine A_n-formality for number fields  (2610.11390 - Pál et al., 8 Oct 2026) in Section 1, Introduction