2012/10/17 by Michael J. Hopkins, Hopkins, Michael, Kirsten Wickelgren +1 · 1 citation
Mathematics · #12G06 #55S30 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1210.4964
openalex publication_date 2012/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.