Compositio Mathematica

The Grothendieck conjecture for affine curves

a1 Research Institute for Mathematical Sciences, Kyoto 606-01, Japan; e-mail:

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tamagawa a   [Google Scholar] 


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.