On the birational section conjecture over finitely generated fields

TL;DR

This paper explores the birational section conjecture for curves over function fields of characteristic zero, establishing that its validity over number fields extends to finitely generated fields over Q.

Contribution

It proves that the birational section conjecture over finitely generated fields over Q follows from its validity over number fields.

Findings

The conjecture holds over finitely generated fields if it holds over number fields.

Extension of the conjecture's validity from number fields to finitely generated fields.

Provides a link between the conjecture's validity over different types of fields.

Abstract

We investigate the birational section conjecture for curves over function fields of characteristic zero and prove that the conjecture holds over finitely generated fields over Q if it holds over number fields.