Affine anabelian curves in positive characteristic
arXiv:math/0206188
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 π^{tame} of curves over a finitely generated field and its effect on the set of isomorphisms. Universal homeomorphisms are formally inverted.
LaTeX, 10 pages, to appear in Compositio Mathematica