Splitting varieties for triple Massey products
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Publication:2254311
DOI10.1016/J.JPAA.2014.06.006zbMATH Open1323.55014arXiv1210.4964OpenAlexW2059731743MaRDI QIDQ2254311
Author name not available (Why is that?)
Publication date: 4 February 2015
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/1210.4964
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