Cohomology of the geometric fundamental group of hyperbolic polycurves
Cohomology of the geometric fundamental group of hyperbolic polycurves
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双曲多重曲线几何基本群的上同调
DOI：
10.1016/j.jalgebra.2018.04.028
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发表时间：
2018
影响因子：
0.9
通讯作者：
Sawada Koichiro
中科院分区：
文献类型：
--
作者：
Okamoto A;Shimada M;Yamashita Y;Sawada Koichiro
在本文中，我们研究了通过 (pro-Σ) 表面群族的连续扩展获得的有限群的上同调群。作为一个应用，我们展示了特征零域上的双曲多重曲线（即双曲曲线族的连续扩展）的维数可以从其几何基本群进行群论重建。
In the present paper, we study the cohomology groups of profinite groups obtained by successive extensions of families of (pro-Σ) surface groups. As an application, we show, among others, that the dimension of a hyperbolic polycurve (i.e., a successive extension of a family of hyperbolic curves) over a field of characteristic zero can be reconstructed group-theoretically from its geometric fundamental group.