Triple Massey products of weight (1,n,1) in Galois cohomology

Triple Massey products and absolute Galois groups

“…In the recent paper [MT14c] (which was posted after the initial version [Mat14] of the current work) Mináč and Tân also give a Galois-cohomological proof of the Main Theorem, which is similar at several points to our proof; See also [MT15]. Moreover, they point out that the standard restriction-correstriction argument allows one to remove the assumption that the field contains a root of unity of order p. Namely, for a pth root of unity ζ, the index of U = G F (ζ) in G = G F is prime to p. If χ 1 , χ 2 , χ 3 ∈ H 1 (G) and α ∈ χ 1 , χ 2 , χ 3 , then by our Main Theorem,…”

“…The Main Theorem was first proved by the second-named author using methods from the theory of central simple algebras, notably the AmitsurSaltman theory of abelian crossed products [Mat14]. The current paper, which replaces [Mat14], is based on a shortcut which allows carrying the original crossed product computations to the framework of profinite group cohomology (see Proposition 5.3).…”

“…The current paper, which replaces [Mat14], is based on a shortcut which allows carrying the original crossed product computations to the framework of profinite group cohomology (see Proposition 5.3). We also work in a more general formal context, and prove the Main Theorem for p-Kummer formations (G, A, {κ U } U ) (Theorem 5.4).…”

Triple Massey products vanish over all fields

“…In [8], Efrat and Matzri provided alternative proofs for the above-mentioned results in [17,19]. In [14], Matzri proved that, for any prime p and for any field F containing a primitive pth root of unity, G F has the vanishing triple Massey product property. In this paper, we shall provide a cohomological proof to the main result in [14] (see Theorem 4.10).…”

“…In [14], Matzri proved that, for any prime p and for any field F containing a primitive pth root of unity, G F has the vanishing triple Massey product property. In this paper, we shall provide a cohomological proof to the main result in [14] (see Theorem 4.10). We also remove the assumption that F contains a primitive pth root of unity (see Theorem 4.15).…”