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arXiv · 1011.1419

Subgroups of profinite surface groups

Lior Bary-Soroker·Katherine F. Stevenson·Pavel Zalesskii
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Abstract

We study the subgroup structure of the étale fundamental group $Π$ of a projective curve over an algebraically closed field of characteristic 0. We obtain an analog of the diamond theorem for $Π$. As a consequence we show that most normal subgroups of infinite index are semi-free. In particular every proper open subgroup of a normal subgroup of infinite index is semi-free.

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Lior Bary-Soroker, Katherine F. Stevenson, Pavel Zalesskii. 2010-11-05. Subgroups of profinite surface groups. https://arxiv.org/abs/1011.1419

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