The real section conjecture and Smith's fixed point theorem for pro-spaces

Details The real section conjecture and Smith's fixed point theorem for pro-spaces The real section conjecture and Smith's fixed point theorem for pro-spaces

2009-05-08

arxiv.org/abs/0905.1205v2

Mathematics

Number Theory

assumptions of the main results are changed, an error in the proof is corrected, a section on good groups is added

Scientific paper

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 $p$ whose $p$-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.

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