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Massey products <y,x,x,...,x,x,y> in Galois cohomology via rational points

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Preprint
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Submission Date
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arXiv ID: 1601.06318
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arXiv
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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 $\pi_1$ applied to this embedding to unipotent matrix groups. This method produces obstructions to $\pi_1$-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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