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  Journal of Algebraic Geometry
Journal of Algebraic Geometry
  
Online ISSN 1534-7486; Print ISSN 1056-3911
 

Finiteness of isomorphism classes of curves in positive characteristic with prescribed fundamental groups


Author: Akio Tamagawa
Translated by:
Journal: J. Algebraic Geom. 13 (2004), 675-724
Published electronically: February 25, 2004
MathSciNet review: 2073193
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Abstract | References | Additional Information

Abstract: We prove that there are only finitely many isomorphism classes of smooth, hyperbolic curves over an algebraic closure of the finite prime field $\mathbb{F} _{p}$, whose (tame) fundamental group is isomorphic to a prescribed profinite group. This is a generalization of partial results by Pop, Saïdi and Raynaud. The key ingredient of the proof is Raynaud's theory of theta divisors. In course of the proof, we also obtain some results concerning gonalities of coverings of curves and concerning the infinitesimal Torelli problem for generalized Prym varieties, which are applicable to arbitrary (not necessarily positive) characteristic and may be of some interest independent of the study of fundamental groups of curves in positive characteristic.


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Additional Information

Akio Tamagawa
Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
Email: tamagawa@kurims.kyoto-u.ac.jp

DOI: http://dx.doi.org/10.1090/S1056-3911-04-00376-5
PII: S 1056-3911(04)00376-5
Received by editor(s): May 1, 2002
Published electronically: February 25, 2004


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