Massey products 〈y,x,x,…,x,x,y〉 in Galois cohomology via rational points

Abstract

For x an element of a field other than 0 or 1, we compute the order n Massey products〈(1−x)−1,x−1,…,x−1,(1−x)−1〉 of n−2 factors of x−1 and two factors of (1−x)−1 by embedding P1−{0,1,∞} into its Picard variety and constructing Gal(ks/k) equivariant maps from π1et applied to this embedding to unipotent matrix groups. This method produces obstructions to π1-sections of P1−{0,1,∞}, partial computations of obstructions of Jordan Ellenberg, and also computes the Massey products〈x−1,(−x)−1,…,(−x)−1,x−1〉.