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On the Tame Fundamental Groups of Curves over Algebraically Closed Fields of Characteristic > 0

By Akio Tamagawa

Abstract

We prove that the isomorphism class of the tame fundamental group of a smooth, connected curve over an algebraically closed field k of characteristic p > 0 determines the genus g and the number n of punctures of the curve, unless (g, n) = (0, 0), (0, 1). Moreover, assuming g = 0, n > 1, and that k is the algebraic closure of the prime field Fp, we prove that the isomorphism class of the tame fundamental group even completely determines the isomorphism class of the curve as a scheme (though not necessarily as a k-scheme). As a key tool to prove these results, we generalize Raynaud's theory of theta divisors

Year: 2003
OAI identifier: oai:CiteSeerX.psu:10.1.1.170.9066
Provided by: CiteSeerX

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