On 3-nilpotent obstructions to π1 sections for ℙ1 ℚ-{0,1,∞}


Book Section

© Springer-Verlag Berlin Heidelberg 2012. We study which rational points of the Jacobian of ℙ1-{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(Gk, ℤ(1)) or H1(Gk,ℤ/2ℤ). For k = ℚp or 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.

Full Text

Duke Authors

Cited Authors

  • Wickelgren, K

Published Date

  • January 1, 2012

Book Title

  • The Arithmetic of Fundamental Groups: PIA 2010

Start / End Page

  • 281 - 328

International Standard Book Number 13 (ISBN-13)

  • 9783642239045

Digital Object Identifier (DOI)

  • 10.1007/978-3-642-23905-2_12

Citation Source

  • Scopus