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

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An Erratum to this article was published on 17 May 2014

Abstract

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 (respectively, characteristic) subgroup of π 1(C). Under the hypothesis that the quotient π 1(C)/N admits an infinitely generated Sylow p-subgroup, we prove that N is indeed isomorphic to a normal (respectively, 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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Authors and Affiliations

  1. Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rua Guaiaquil 83, Cachambi, Rio de Janeiro, RJ, 20785-050, Brazil

    Amílcar Pacheco

  2. Department of Mathematics, California State University, Northridge, CA, 91330, USA

    Katherine F. Stevenson

  3. Departamento de Matemática, Universidade de Brasília, Brasília, DF, 70910-900, Brazil

    Pavel Zalesskii

Authors
  1. Amílcar Pacheco
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  2. Katherine F. Stevenson
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  3. Pavel Zalesskii
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Corresponding author

Correspondence to Amílcar Pacheco.

Additional information

Amílcar Pacheco and Pavel Zalesskii were partially supported by CNPq research grants 305731/2006-8 and 307823/2006-7, respectively. They were also supported by Edital Universal CNPq 471431/2006-0.

An erratum to this article is available at http://dx.doi.org/10.1007/s00208-014-1051-5.

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Pacheco, A., Stevenson, K.F. & Zalesskii, P. Normal subgroups of the algebraic fundamental group of affine curves in positive characteristic. Math. Ann. 343, 463–486 (2009). https://doi.org/10.1007/s00208-008-0279-3

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  • DOI: https://doi.org/10.1007/s00208-008-0279-3

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