Abstract
We study which rational points of the Jacobian of ℙ 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 , ℤ(1)) or H1(G k , ℤ ∕ 2ℤ). For k = ℚ p or \(\mathbb{R}\), we give a complete mod 2 calculation. This permits some mod 2 calculations for k = ℚ. These are computations of obstructions of Jordan Ellenberg. ℙ1ℚ − { 0, 1, ∞}
Supported by an NSF Graduate Research Fellowship, a Stanford Graduate Fellowship, and an American Institute of Math Five Year Fellowship
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Wickelgren, K. (2012). On 3-Nilpotent Obstructions to π1 Sections for \( \mathbb{P}^{1}_\mathbb{Q}\)−{0,1, \(\infty\)}. In: Stix, J. (eds) The Arithmetic of Fundamental Groups. Contributions in Mathematical and Computational Sciences, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23905-2_12
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DOI: https://doi.org/10.1007/978-3-642-23905-2_12
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