The local-global principle for integral points on stacky curves

IF 0.9 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry Pub Date : 2020-05-30 DOI:10.1090/jag/796

M. Bhargava, B. Poonen

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引用次数: 7

Abstract

We construct a stacky curve of genus 1 / 2 1/2 (i.e., Euler characteristic 1 1 ) over Z \mathbb {Z} that has an R \mathbb {R} -point and a Z p \mathbb {Z}_p -point for every prime p p but no Z \mathbb {Z} -point. This is best possible: we also prove that any stacky curve of genus less than 1 / 2 1/2 over a ring of S S -integers of a global field satisfies the local-global principle for integral points.

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叠曲线上积分点的局部-全局原理

我们在Z \mathbb {Z}上构造了一个1/2 /2属(即欧拉特征1 1)的曲线，对于每一个素数p p都有一个R \mathbb {R}点和一个Z p \mathbb {Z}_p点，但没有Z \mathbb {Z}点。这是最好的可能:我们还证明了在全局域的S -整数环上，任何属小于1/2 1/2的叠曲线都满足积分点的局部-全局原理。

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来源期刊

Journal of Algebraic Geometry 数学-数学

CiteScore

2.70

自引率

5.60%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology. This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.