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

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 $p$ 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.

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

References in corpus (1)

• On the period-index problem in light of the section conjecture

Cited by in corpus (4)

• 2-Nilpotent Real Section Conjecture
• Anabelian geometry and descent obstructions on moduli spaces
• Continuous group actions on profinite spaces
• An elementary approach to Stix's proof of the real section conjecture