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arXiv · 1106.6004

Subgroup structure of fundamental groups in positive characteristic

Lior Bary-Soroker·Manish Kumar
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Abstract

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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Lior Bary-Soroker, Manish Kumar. 2011-06-29. Subgroup structure of fundamental groups in positive characteristic. https://arxiv.org/abs/1106.6004

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