实截猜想与Pro-空间的Smith不动点定理
The real section conjecture and Smith's fixed point theorem for pro-spaces
摘要：
我们证明了一个拓扑版本的部分猜想的profinite完成的基本群的有限CW-复配备了一组素数阶$p$的作用，其$p$ -扭转上同调可以杀死有限覆盖。作为应用，我们得到了实数域上一大类簇的实点的截口猜想，以及复数域上正亏格的射影曲线上有限群作用的不动点的截口猜想的自然类比.
英文摘要：
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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