Abstract
An investigation of morphisms that coincide topologically is used to generalize to all characteristics and partly reprove Tamagawa's theorem on the Grothendieck conjecture in anabelian geometry for affine hyperbolic curves. The theorem now deals with π1 tame of curves over a finitely generated field and its effect on the sets of isomorphisms. Universal homeomorphisms are formally inverted.
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Stix, J. Affine Anabelian Curves in Positive Characteristic. Compositio Mathematica 134, 75–85 (2002). https://doi.org/10.1023/A:1020290619656
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DOI: https://doi.org/10.1023/A:1020290619656