Fundamental group 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.
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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.
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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 ...
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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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Morgenstern ([Mor95]) claimed to have constructed fundamental domains for congruence subgroups of the lattice group Γ = PGL2(Fq[t]), and subgraphs providing the first known examples of linear families of bounded concentrators. His method was to construct the fundamental domain for a congruence subgroup as a ‘ramified covering’ of the fundamental domain for Γ on the Bruhat-Tits tree X = Xq+1 of ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2008
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2008.01.013