On The Hom-Form of Grothendieck's Birational Anabelian Conjecture in Characteristic p>0

TL;DR

This paper proves that specific open homomorphisms between Galois groups of function fields over finite fields originate from embeddings of the fields themselves, advancing understanding of anabelian geometry in characteristic p>0.

Contribution

It establishes a hom-form version of Grothendieck's birational anabelian conjecture for function fields over finite fields in characteristic p>0.

Findings

Open homomorphisms correspond to field embeddings.

Results extend anabelian geometry to positive characteristic.

Provides new insights into Galois group structures in algebraic geometry.

Abstract

We prove that a certain class of open homomorphisms between Galois groups of function fields of curves over finite fields arise from embeddings between the function fields.