The localglobal principle for integral points on stacky curves
Abstract
We construct a stacky curve of genus $1/2$ (i.e., Euler characteristic $1$) over $\mathbb{Z}$ that has an $\mathbb{R}$point and a $\mathbb{Z}_p$point for every prime $p$ but no $\mathbb{Z}$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 localglobal principle for integral points.
 Publication:

arXiv eprints
 Pub Date:
 May 2020
 DOI:
 10.48550/arXiv.2006.00167
 arXiv:
 arXiv:2006.00167
 Bibcode:
 2020arXiv200600167B
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Algebraic Geometry;
 11G30 (Primary) 14A20;
 14G25;
 14H25 (Secondary)
 EPrint:
 9 pages