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# Vanishing of Massey Products and Brauer Groups

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Published:2015-05-21
Printed: Dec 2015
• Ido Efrat,
Department of Mathematics, Ben-Gurion University of the Negev, Be'er-Sheva 84105, Israel
• Eliyahu Matzri,
Department of Mathematics, Ben-Gurion University of the Negev, Be'er-Sheva 84105, Israel
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## Abstract

Let $p$ be a prime number and $F$ a field containing a root of unity of order $p$. We relate recent results on vanishing of triple Massey products in the mod-$p$ Galois cohomology of $F$, due to Hopkins, Wickelgren, Mináċ, and Tân, to classical results in the theory of central simple algebras. For global fields, we prove a stronger form of the vanishing property.
 Keywords: Galois cohomology, Brauer groups, triple Massey products, global fields
 MSC Classifications: 16K50 - Brauer groups [See also 12G05, 14F22] 11R34 - Galois cohomology [See also 12Gxx, 19A31] 12G05 - Galois cohomology [See also 14F22, 16Hxx, 16K50] 12E30 - Field arithmetic

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