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arXiv · 1601.06318

Massey products in Galois cohomology via rational points

Kirsten Wickelgren
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Abstract

For $x$ an element of a field other than $0$ or $1$, we compute the order $n$ Massey products $$\langle (1-x)^{-1}, x^{-1}, \ldots, x^{-1}, (1-x)^{-1} \rangle$$ of $n-2$ factors of $x^{-1}$ and two factors of $(1-x)^{-1}$ by embedding $\mathbb{P}^1 - \{0,1,\infty\}$ into its Picard variety and constructing $\operatorname{Gal}(k^s/k)$ equivariant maps from $π_1$ applied to this embedding to unipotent matrix groups. This method produces obstructions to $π_1$-sections of $\mathbb{P}^1 - \{0,1,\infty\}$, partial computations of obstructions of Jordan Ellenberg, and also computes the Massey products $$\langle x^{-1} , (-x)^{-1}, \ldots, (-x)^{-1}, x^{-1} \rangle.$$

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Kirsten Wickelgren. 2016-09-12. Massey products in Galois cohomology via rational points. https://arxiv.org/abs/1601.06318

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