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

TL;DR

This paper refines Uchida's theorem by demonstrating isomorphisms between absolute Galois groups of global fields over finite fields, ignoring a small set of primes, advancing understanding of anabelian geometry in positive characteristic.

Contribution

It introduces a refined version of Uchida's theorem that accounts for a limited set of primes, enhancing the understanding of Galois group isomorphisms over finite fields.

Findings

Proves a refined isomorphism theorem for Galois groups

Shows the impact of ignoring small prime sets on Galois correspondence

Advances the theory of anabelian geometry in positive characteristic

Abstract

In this paper we prove a refined version of Uchida's theorem on isomorphisms between absolute Galois groups of global fields in positive characteristics, where one "ignores" the information provided by a "small" set of primes.