The fundamental group of affine curves in positive characteristic
نویسندگان
چکیده
منابع مشابه
The Fundamental Group of Affine Curves in Positive Characteristic
It is shown that the commutator subgroup of the fundamental group of a smooth irreducible affine curve over an uncountable algebraically closed field k of positive characteristic is a profinite free group of rank equal to the cardinality of k.
متن کاملNormal Subgroups of the Algebraic Fundamental Group of Affine Curves in Positive Characteristic
Let π1(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 π1(C). Under the hypothesis that the quotient π1(C)/N admits an infinitely generated Sylow p-subgroup, we prove that N is indeed isomorphic to a normal (resp. characteris...
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Let X be a smooth projective connected algebraic curve of genus g defined over an algebraically closed field k of characteristic p > 0. In this paper we study necessary and sufficient conditions for a finite group G to be a quotient of the algebraic fundamental group π1(X) of X. We denote by πA(X) the set of isomorphism classes of finite groups which are quotients of π1(X). Recall that a group ...
متن کاملFundamental Group in Nonzero Characteristic
A proof of freeness of the commutator subgroup of the fundamental group of a smooth irreducible affine curve over a countable algebraically closed field of nonzero characteristic. A description of the abelianizations of the fundamental groups of affine curves over an algebraically closed field of nonzero characteristic is also given.
متن کاملOn the Specialization Homomorphism of Fundamental Groups of Curves in Positive Characteristic
Introduction Recall that for proper smooth and connected curves of genus g ≥ 2 over an algebraically closed eld of characteristic 0 the structure of the étale fundamental group π g is well known and depends only on the genus g. Namely it is the pro-nite completion of the topological fundamental group of a compact orientable topological surface of genus g. In contrast to this, the structure of t...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2014
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2013.10.007