2-Nilpotent Real Section Conjecture

Details 2-Nilpotent Real Section Conjecture 2-Nilpotent Real Section Conjecture

2010-06-01

arxiv.org/abs/1006.0265v2

Mathematics

Algebraic Geometry

29 pages, 1 figure. The main result now holds for singular curves as well. The article is completely rewritten

Scientific paper

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, pi_0(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 the maximal 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.

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