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

Creators: Pacheco, Amilcar; Stevenson, Katherine F.

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.

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.

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