Journal of the European Mathematical Society


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Volume 19, Issue 12, 2017, pp. 3629–3640
DOI: 10.4171/JEMS/748

Published online: 2017-11-20

Triple Massey products and absolute Galois groups

Ido Efrat[1] and Eliyahu Matzri[2]

(1) Ben Gurion University of the Negev, Beer-Sheva, Israel
(2) Ben Gurion University of the Negev, Beer-Sheva, Israel

Let $p$ be a prime number, $F$ a field containing a root of unity of order $p$, and $G_F$ the absolute Galois group. Extending results of Hopkins, Wickelgren, Mináč and Tân, we prove that the triple Massey product $H^1(G_F)^3\to H^2(G_F)$ contains 0 whenever it is non-empty. This gives a new restriction on the possible profinite group structure of $G_F$.

Keywords: Triple Massey products, absolute Galois groups, Galois cohomology

Efrat Ido, Matzri Eliyahu: Triple Massey products and absolute Galois groups. J. Eur. Math. Soc. 19 (2017), 3629-3640. doi: 10.4171/JEMS/748