The Brauer-Manin obstruction for nonisotrivial curves over global function fields

TL;DR

This paper proves that for nonisotrivial curves of genus at least 2 over global function fields, the Brauer-Manin obstruction precisely characterizes the set of rational points, extending understanding of rational solutions in this context.

Contribution

It establishes that the Brauer-Manin obstruction fully accounts for rational points on certain nonisotrivial curves over global function fields, a significant advance in arithmetic geometry.

Findings

The set of rational points equals the Brauer-Manin set for these curves.

The result applies to nonisotrivial curves of genus at least 2.

It confirms the effectiveness of the Brauer-Manin obstruction in this setting.

Abstract

We prove that the set of rational points on a nonisotrivial curves of genus at least 2 over a global function field is equal to the set of adelic points cut out by the Brauer-Manin obstruction.