Subgroups of profinite surface groups

Details Subgroups of profinite surface groups Subgroups of profinite surface groups

2010-11-05

arxiv.org/abs/1011.1419v1

Mathematics

Group Theory

Scientific paper

We study the subgroup structure of the \'etale fundamental group $\Pi$ of a
projective curve over an algebraically closed field of characteristic 0. We
obtain an analog of the diamond theorem for $\Pi$. 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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