2-Nilpotent real section conjecture

Journal Article

We show a 2-nilpotent section conjecture over ℝ: for a geometrically connected curve X over ℝ such that each irreducible component of its normalization has ℝ-points, π0(X(ℝ)) is determined by the maximal 2-nilpotent quotient of the fundamental group with its Galois action, as the kernel of an obstruction of Jordan Ellenberg. This implies that for X smooth and proper, X(ℝ)± is determined by themaximal 2-nilpotent quotient of Gal(ℂ(X)) with its Gal(ℝ) action, where X(ℝ)± denotes the set of real points equipped with a real tangent direction, showing a 2-nilpotent birational real section conjecture. © 2013 Springer-Verlag Berlin Heidelberg.

Full Text

Duke Authors

Cited Authors

  • Wickelgren, K

Published Date

  • January 1, 2014

Published In

Volume / Issue

  • 358 / 1-2

Start / End Page

  • 361 - 387

International Standard Serial Number (ISSN)

  • 0025-5831

Digital Object Identifier (DOI)

  • 10.1007/s00208-013-0967-5

Citation Source

  • Scopus