Local-global principles for semi-integral points on Markoff orbifold pairs

Vladimir Mitankin; Justin Uhlemann

doi:10.48550/arXiv.2411.02629

Local-global principles for semi-integral points on Markoff orbifold pairs

Vladimir Mitankin
, Justin Uhlemann

Research output: Working paper › Preprint › Academic

Abstract

We study local-global principles for semi-integral points on orbifold pairs of Markoff type. In particular, we analyse when these orbifold pairs satisfy weak weak approximation, weak approximation and strong approximation off a finite set of places. We show that Markoff orbifold pairs satisfy the semi-integral Hasse principle and we measure how often such orbifold pairs have strict semi-integral points but the corresponding Markoff surface lacks integral points.

Original language	English
Publisher	arXiv
Number of pages	28
DOIs	https://doi.org/10.48550/arXiv.2411.02629
Publication status	Published - 6 Nov 2024

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Name	arXiv
ISSN (Print)	2331-8422

Funding

Supported by NWO grant VI.Vidi.213.019.

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10.48550/arXiv.2411.02629Licence: CC BY

2411.02629v2Submitted manuscript, 350 KBLicence: CC BY

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AB - We study local-global principles for semi-integral points on orbifold pairs of Markoff type. In particular, we analyse when these orbifold pairs satisfy weak weak approximation, weak approximation and strong approximation off a finite set of places. We show that Markoff orbifold pairs satisfy the semi-integral Hasse principle and we measure how often such orbifold pairs have strict semi-integral points but the corresponding Markoff surface lacks integral points.

U2 - 10.48550/arXiv.2411.02629

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M3 - Preprint

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PB - arXiv

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Local-global principles for semi-integral points on Markoff orbifold pairs

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