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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



The local-global principle for integral points on stacky curves

Authors: Manjul Bhargava and Bjorn Poonen
Journal: J. Algebraic Geom. 31 (2022), 773-782
Published electronically: May 31, 2022
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Abstract | References | Additional Information

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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Additional Information

Manjul Bhargava
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
MR Author ID: 623882

Bjorn Poonen
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307
MR Author ID: 250625
ORCID: 0000-0002-8593-2792

Received by editor(s): June 22, 2020
Published electronically: May 31, 2022
Additional Notes: The first author was supported in part by National Science Foundation grant DMS-1001828 and Simons Foundation grant #256108. The second author was supported in part by National Science Foundation grants DMS-1601946 and DMS-2101040 and Simons Foundation grants #402472 and #550033.
Article copyright: © Copyright 2022 University Press, Inc.