Affine anabelian curves in positive characteristic

TL;DR

This paper generalizes Tamagawa's theorem on the Grothendieck conjecture for affine hyperbolic curves to all characteristics, using morphisms that coincide topologically and considering tame fundamental groups.

Contribution

It extends anabelian geometry results to positive characteristic by analyzing topological morphisms and inverting universal homeomorphisms, providing a broader proof framework.

Findings

Generalization of Tamagawa's theorem to all characteristics

Inversion of universal homeomorphisms in the proof

Enhanced understanding of tame fundamental groups in positive characteristic

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 \pi^{tame} of curves over a finitely generated field and its effect on the set of isomorphisms. Universal homeomorphisms are formally inverted.