A refined version of Grothendieck's anabelian conjecture for hyperbolic curves over finite fields

TL;DR

This paper refines a theorem on the isomorphisms of arithmetic fundamental groups of hyperbolic curves over finite fields, focusing on the impact of ignoring a small set of primes, advancing understanding in anabelian geometry.

Contribution

It provides a refined version of Tamagawa and Mochizuki's theorem, specifically addressing the role of small prime sets in fundamental group isomorphisms over finite fields.

Findings

Refined theorem for hyperbolic curves over finite fields

Shows isomorphisms hold when ignoring small prime sets

Advances understanding of anabelian geometry in finite fields

Abstract

In this paper we prove a refined version of a theorem by Tamagawa and Mochizuki on isomorphisms between (tame) arithmetic fundamental groups of hyperbolic curves over finite fields, where one "ignores" the information provided by a "small" set of primes.