We construct a stacky curve of genus 1/2 (i.e., Euler characteristic 1) over Z that has an R-point and a Zp-point for every prime p but no Z-point. This is best possible: we also prove that any stacky curve of genus less than 1/2 over a ring of S-integers of a global field satisfies the local-global principle for integral points.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Geometry and Topology