The local-global principle for integral points on stacky curves

Abstract

We construct a stacky curve of genus 1 / 2 1/2 (i.e., Euler characteristic  1 1 ) over Z \mathbb {Z} that has an R \mathbb {R} -point and a Z p \mathbb {Z}_p -point for every prime p p but no Z \mathbb {Z} -point. This is best possible: we also prove that any stacky curve of genus less than 1 / 2 1/2 over a ring of S S -integers of a global field satisfies the local-global principle for integral points.