THE LOCAL-GLOBAL PRINCIPLE for INTEGRAL POINTS on STACKY CURVES

Manjul Bhargava; Bjorn Poonen

doi:10.1090/jag/796

THE LOCAL-GLOBAL PRINCIPLE for INTEGRAL POINTS on STACKY CURVES

Manjul Bhargava, Bjorn Poonen

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Pages (from-to)	773-782
Number of pages	10
Journal	Journal of Algebraic Geometry
Volume	31
Issue number	4
DOIs	https://doi.org/10.1090/jag/796
State	Published - 2022

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Geometry and Topology

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10.1090/jag/796

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title = "THE LOCAL-GLOBAL PRINCIPLE for INTEGRAL POINTS on STACKY CURVES",

abstract = "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.",

author = "Manjul Bhargava and Bjorn Poonen",

note = "Funding Information: Received June 22, 2020. 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. Publisher Copyright: {\textcopyright} 2022 University Press, Inc.",

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doi = "10.1090/jag/796",

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journal = "Journal of Algebraic Geometry",

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N2 - 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.

AB - 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.

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THE LOCAL-GLOBAL PRINCIPLE for INTEGRAL POINTS on STACKY CURVES

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