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arXiv · 2208.13011

Degenerate fourfold Massey products over arbitrary fields

Alexander Merkurjev·Federico Scavia
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Abstract

We prove that, for all fields $F$ of characteristic different from $2$ and all $a,b,c\in F^\times$, the mod $2$ Massey product $\langle a,b,c,a \rangle$ vanishes as soon as it is defined. For every field $F_0$, we construct a field $F$ containing $F_0$ and $a,b,c,d\in F^\times$ such that $\langle a,b,c \rangle$ and $\langle b,c,d \rangle$ vanish but $\langle a,b,c,d \rangle$ is not defined. As a consequence, we answer a question of Positselski by constructing the first examples of fields containing all roots of unity and such that the mod $2$ cochain DGA of the absolute Galois group is not formal.

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Alexander Merkurjev, Federico Scavia. 2022-08-27. Degenerate fourfold Massey products over arbitrary fields. https://arxiv.org/abs/2208.13011

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