**Papers Published**

- Hopkins, MJ; Wickelgren, KG,
*Splitting varieties for triple Massey products*, Journal of Pure and Applied Algebra, vol. 219 no. 5 (May, 2015), pp. 1304-1319

(last updated on 2022/08/07)**Abstract:**

We construct splitting varieties for triple Massey products. For a, b, c∈F* the triple Massey product 〈a, b, c〉 of the corresponding elements of H1(F, μ2) contains 0 if and only if there are x∈F* and y∈F[a,c]* such that bx2=NF[a,c]/F(y), where NF[a,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. Leep and A.R. Wadsworth. This shows that triple Massey products for global fields of characteristic different from 2 always contain 0.