Mathematical Research Letters
Volume 18 (2011)
Subgroups of profinite surface groups
Pages: 459 – 471
We study the subgroup structure of the étale 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.