Massey products in Galois cohomology and Pythagorean fields

Abstract

We prove that a strengthened version of Minac-Tan's Massey Vanishing Conjecture holds true for fields with a finite number of square classes whose maximal pro-$2$ Galois group is of elementary type (as defined by I. Efrat). In particular, this proves Minac-Tan's Massey Vanishing Conjecture for Pythagorean fields with a finite number of square classes and their finite extensions.

Final version, to appear on "Communications in Algebra". Minor changes from the previous version. arXiv admin note: text overlap with arXiv:2203.16232