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

1 Scopus citations

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

Access to Document

10.1090/jag/796

Cite this

@article{134207c7dec1411792242ad1d92a45dd,

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 = "Publisher Copyright: {\textcopyright} 2022 University Press, Inc.",

year = "2022",

doi = "10.1090/jag/796",

language = "English (US)",

volume = "31",

pages = "773--782",

journal = "Journal of Algebraic Geometry",

issn = "1056-3911",

publisher = "American Mathematical Society",

number = "4",

}

TY - JOUR

T1 - THE LOCAL-GLOBAL PRINCIPLE for INTEGRAL POINTS on STACKY CURVES

AU - Bhargava, Manjul

AU - Poonen, Bjorn

PY - 2022

Y1 - 2022

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.

UR - http://www.scopus.com/inward/record.url?scp=85138261855&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85138261855&partnerID=8YFLogxK

U2 - 10.1090/jag/796

DO - 10.1090/jag/796

M3 - Article

AN - SCOPUS:85138261855

SN - 1056-3911

VL - 31

SP - 773

EP - 782

JO - Journal of Algebraic Geometry

JF - Journal of Algebraic Geometry

IS - 4

ER -

THE LOCAL-GLOBAL PRINCIPLE for INTEGRAL POINTS on STACKY CURVES

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this