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arXiv · 2006.00167

The local-global principle for integral points on stacky curves

Manjul Bhargava·Bjorn Poonen
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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 local-global principle for integral points.

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Manjul Bhargava, Bjorn Poonen. 2020-05-30. The local-global principle for integral points on stacky curves. https://arxiv.org/abs/2006.00167

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