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
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实部猜想和史密斯原空间不动点定理
DOI：
10.1112/jlms/jdq075
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Pál A
中科院分区：
文献类型：
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作者：
Pál A
我们证明了截面猜想的拓扑版本，用于有限 CW 复形的基本群的有限完备性，该群配备了一组素阶 p 扭转上同调的作用，可以通过有限覆盖来消除。作为一个应用，我们推导出实数域上定义的一大类簇的实点的截面猜想，以及复数域上定义的正亏格射影曲线上有限群作用不动点的截面猜想的自然类比。
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 orderpwhosep‐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.