**Papers Published**

- Wickelgren, K,
*2-Nilpotent real section conjecture*, Mathematische Annalen, vol. 358 no. 1-2 (February, 2014), pp. 361-387

(last updated on 2022/08/07)**Abstract:**

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.