Splitting Varieties for Triple Massey Products
Algebraic Topology
2014-05-30 v2 Number Theory
Abstract
We construct splitting varieties for triple Massey products. For a,b,c in F^* the triple Massey product < a,b,c> of the corresponding elements of H^1(F, mu_2) contains 0 if and only if there is x in F^* and y in F[\sqrt{a}, \sqrt{c}]^* such that b x^2 = N_{F[\sqrt{a}, \sqrt{c}]/F}(y), where N_{F[\sqrt{a}, \sqrt{c}]/F} denotes the norm, and F is a field of characteristic different from 2. These varieties satisfy the Hasse principle by a result of D.B. Lee and A.R. Wadsworth. This shows that triple Massey products for global fields of characteristic different from 2 always contain 0.
Cite
@article{arxiv.1210.4964,
title = {Splitting Varieties for Triple Massey Products},
author = {Michael Hopkins and Kirsten Wickelgren},
journal= {arXiv preprint arXiv:1210.4964},
year = {2014}
}
Comments
18 pages. To appear in Journal of Pure and Applied Algebra