Splitting Varieties for Triple Massey Products
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 H1(F, mu2) contains 0 if and only if there is x in F* and y in F[a, c]* such that b x2 = 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. Lee and A.R. Wadsworth. This shows that triple Massey products for global fields of characteristic different from 2 always contain 0.
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