Normal subgroups of the algebraic fundamental group of affine curves in positive characteristic

Details Normal subgroups of the algebraic fundamental group of affine curves in positive characteristic Normal subgroups of the algebraic fundamental group of affine curves in positive characteristic

2007-10-28

arxiv.org/abs/0710.5279v3

Mathematics

Algebraic Geometry

A hypothesis has been added to Theorem 1.1

Scientific paper

Let $\pi_1(C)$ be the algebraic fundamental group of a smooth connected affine curve, defined over an algebraically closed field of characteristic $p>0$ of countable cardinality. Let $N$ be a normal (resp. characteristic) subgroup of $\pi_1(C)$. Under the hypothesis that the quotient $\pi_1(C)/N$ admits an infinitely generated Sylow $p$-subgroup, we prove that $N$ is indeed isomorphic to a normal (resp. characteristic) subgroup of a free profinite group of countable cardinality. As a consequence, every proper open subgroup of $N$ is a free profinite group of countable cardinality.

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