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Finite quotients of the algebraic fundamental group of projective curves in positive characteristic

Pacheco, Amilcar and Stevenson, Katherine F. (2000) Finite quotients of the algebraic fundamental group of projective curves in positive characteristic. Pacific Journal of Mathematics, 192 (1). pp. 143-158. ISSN 0030-8730. http://resolver.caltech.edu/CaltechAUTHORS:PACpjm00

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Abstract

Let X be a smooth connected projective curve defined over an algebraically closed field k of characteristic p >0. Let G be a finite group whose order is divisible by p. Suppose that G has a normal p-Sylow subgroup. We give a necessary and sufficient condition for G to be a quotient of the algebraic fundamental group pi(1)(X) of X.


Item Type:Article
Additional Information:© Copyright 2000 Pacific Journal of Mathematics. Received May 18, 1998. Amilcar Pacheco was partially supported by CNPq research grant number 300896/91-3 and Pronex, Brazil. Section 5 was partially written during a visit of Amilcar Pacheco to the University of Campinas, Sao Paulo, Brazil. He would like to thank this Institution for its hospitality and Antonio Engler for many conversations. Katherine F. Stevenson was supported by NSA grant MDA 9049710017. Both authors would like to thank David Harbater and his student Rachel Pries for their careful reading and many suggestions on previous versions of this paper.
Subject Keywords:characteristic-p, coverings
Record Number:CaltechAUTHORS:PACpjm00
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:PACpjm00
Alternative URL:http://pjm.math.berkeley.edu/2000/192-1/p08.html
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:624
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:07 Sep 2005
Last Modified:26 Dec 2012 08:40

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