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The Grothendieck conjecture for affine curves

Published online by Cambridge University Press:  04 December 2007

AKIO TAMAGAWA
Affiliation:
Research Institute for Mathematical Sciences, Kyoto 606-01, Japan; e-mail: tamagawa@kurims.kyoto-u.ac.jp
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Abstract

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We prove that the isomorphism class of an affine hyperbolic curve defined over a field finitely generated over ${\bb Q}$ is completely determined by its arithmetic fundamental group. We also prove a similar result for an affine curve defined over a finite field.

Type
Research Article
Copyright
© 1997 Kluwer Academic Publishers