A prime-to-p version of the Grothendieck anabelian conjecture for hyperbolic curves over finite fields of characteristic p>0

TL;DR

This paper proves a prime-to-p version of Grothendieck's anabelian conjecture for hyperbolic curves over finite fields of characteristic p>0, extending previous results by Tamagawa and Mochizuki.

Contribution

It introduces a new prime-to-p perspective on the anabelian conjecture for hyperbolic curves over finite fields, filling a gap in existing proofs.

Findings

Establishes the prime-to-p anabelian correspondence for hyperbolic curves

Extends the scope of Grothendieck's conjecture to new cases

Builds on and generalizes previous full profinite results

Abstract

In this paper, we prove a prime-to-p version of Grothendieck's anabelian conjecture for hyperbolic curves over finite fields of characteristic p>0, whose original (full profinite) version was proved by Tamagawa in the affine case and by Mochizuki in the proper case.