正特征基本群的子群结构
Subgroup structure of fundamental groups in positive characteristic
摘要：
设$Π$是特征为$p>0$的代数闭域上光滑仿射曲线的代数基本群。建立了$Π$闭子群的无穷性的一个判别准则。粗略地说，如果$Π$的一个闭子群在两个正规子群之间被“捕获”，那么它是自由的，只要它包含索引为$p$的大多数开子群。在证明中，我们建立了$Π$的“几乎$ω$ -freeness”的强版本，然后应用Haran-Shapiro归纳法。
英文摘要：
Let $Π$ be the étale fundamental group of a smooth affine curve over an algebraically closed field of characteristic $p>0$. We establish a criterion for profinite freeness of closed subgroups of $Π$. Roughly speaking, if a closed subgroup of $Π$ is "captured" between two normal subgroups, then it is free, provided it contains most of the open subgroups of index $p$. In the proof we establish a strong version of "almost $ω$-freeness" of $Π$ and then apply the Haran-Shapiro induction.
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