Triple Massey products in Galois cohomology

Abstract

Fix an arbitrary prime $p$. Let $F$ be a field, containing a primitive $p$-th root of unity, with absolute Galois group $G_F$. The triple Massey product (in the mod-$p$ Galois cohomology) is a partially defined, multi-valued function $⟨\cdot ,\cdot ,\cdot ⟩:H^1(G_F{)}^3\to H^2(G_F).$ In this work we prove a conjecture made in [11] stating that any defined triple Massey product contains zero. As a result the pro-$p$ groups appearing in [11] are excluded from being absolute Galois groups of fields $F$ as above.

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