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arXiv · 1210.4964

Splitting Varieties for Triple Massey Products

Michael Hopkins·Kirsten Wickelgren
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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.

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Michael Hopkins, Kirsten Wickelgren. 2014-05-29. Splitting Varieties for Triple Massey Products. https://arxiv.org/abs/1210.4964

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