On 3-Nilpotent Obstructions to π1 Sections for \( \mathbb{P}^{1}_\mathbb{Q}\)−{0,1, \(\infty\)}

  • Kirsten Wickelgren
Conference paper
Part of the Contributions in Mathematical and Computational Sciences book series (CMCS, volume 2)


We study which rational points of the Jacobian of k 1 − { 0, 1, } can be lifted to sections of geometrically 3-nilpotent quotients of étale π1 over the absolute Galois group. This is equivalent to evaluating certain triple Massey products of elements of k ⊆ H1(G k , (1)) or H1(G k , ∕ 2). For k = p or \(\mathbb{R}\), we give a complete mod 2 calculation. This permits some mod 2 calculations for k = . These are computations of obstructions of Jordan Ellenberg. 1 − { 0, 1, }


Conjugacy Class Fundamental Group Rational Point Tangential Point Lower Central Series 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Harvard UniversityCambridgeUSA

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