The real section conjecture and Smith's fixed point theorem for pro-spaces
Number Theory
2014-02-26 v2 Algebraic Geometry
Algebraic Topology
Abstract
We prove a topological version of the section conjecture for the profinite completion of the fundamental group of finite CW-complexes equipped with the action of a group of prime order whose -torsion cohomology can be killed by finite covers. As an application we derive the section conjecture for the real points of a large class of varieties defined over the field of real numbers and the natural analogue of the section conjecture for fixed points of finite group actions on projective curves of positive genus defined over the field of complex numbers.
Cite
@article{arxiv.0905.1205,
title = {The real section conjecture and Smith's fixed point theorem for pro-spaces},
author = {Ambrus Pal},
journal= {arXiv preprint arXiv:0905.1205},
year = {2014}
}
Comments
assumptions of the main results are changed, an error in the proof is corrected, a section on good groups is added