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A tubular variant of Runge's method in all dimensions, with applications to integral points on Siegel modular varieties
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Le Fourn, Samuel (2019) A tubular variant of Runge's method in all dimensions, with applications to integral points on Siegel modular varieties. Algebra & Number Theory, 13 (1). pp. 159-209. doi:10.2140/ant.2019.13.159 ISSN 1937-0652.
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Official URL: https://doi.org/10.2140/ant.2019.13.159
Abstract
Runge’s method is a tool to figure out integral points on algebraic curves effectively in terms of height. This method has been generalised to varieties of any dimension, but unfortunately its conditions of application are often too restrictive. In this paper, we provide a further generalisation intended to be more flexible while still effective, and exemplify its applicability by giving finiteness results for integral points on some Siegel modular varieties. As a special case, we obtain an explicit finiteness result for integral points on the Siegel modular variety A2(2).
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Algebraic varieties, Varieties (Universal algebra) | ||||||
| Journal or Publication Title: | Algebra & Number Theory | ||||||
| Publisher: | Mathematical Sciences Publishers | ||||||
| ISSN: | 1937-0652 | ||||||
| Official Date: | 27 March 2019 | ||||||
| Dates: |
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| Volume: | 13 | ||||||
| Number: | 1 | ||||||
| Page Range: | pp. 159-209 | ||||||
| DOI: | 10.2140/ant.2019.13.159 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Reuse Statement (publisher, data, author rights): | First published in Algebra & Number Theory, 13(1), 2019 published by Mathematical Sciences Publishers | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Copyright Holders: | Mathematical Sciences Publishers | ||||||
| Date of first compliant deposit: | 10 October 2018 | ||||||
| Date of first compliant Open Access: | 30 April 2019 | ||||||
| RIOXX Funder/Project Grant: |
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