Massey products \(\langle y,x,x,\ldots ,x,x,y\rangle\) in Galois cohomology via rational points

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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} angle

of

n - 2

factors of

x^{- 1}

and two factors of

(1 - x)^{- 1}

by embedding

m a t h b b P^{1} - 0, 1, i n f t y

into its Picard variety and constructing

o p e r a t o r n a m e G a l (k^{s} / k)

equivariant maps from

p i_{1}

applied to this embedding to unipotent matrix groups. This method produces obstructions to

p i_{1}

-sections of

m a t h b b P^{1} - 0, 1, i n f t y

, partial computations of obstructions of Jordan Ellenberg, and also computes the Massey products

langle x^{-1} , (-x)^{-1}, ldots, (-x)^{-1}, x^{-1} angle.

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