Genus one half stacky curves violating the local-global principle

TL;DR

This paper constructs genus one half stacky curves over number fields that serve as counterexamples to the local-global principle for integral points, highlighting exceptions in arithmetic geometry.

Contribution

It demonstrates the existence of such curves over any number field, providing new counterexamples to the local-global principle in the context of stacky curves.

Findings

Existence of genus one half stacky curves over any number field.

Counterexamples to the local-global principle for integral points.

Construction method applicable to all number fields.

Abstract

For any number field, we prove that there exists a stacky curve of genus one half defined over the ring of its integers violating the local-global principle for integral points.