A tubular variant of Runge’s method in all dimensions, with applications to integral points on Siegel modular varieties

Le Fourn, Samuel

doi:10.2140/ant.2019.13.159

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A tubular variant of Runge's method in all dimensions, with applications to integral points on Siegel modular varieties

Samuel Le Fourn

Vol. 13 (2019), No. 1, 159–209

DOI: 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 generalized to varieties of any dimension, but unfortunately the conditions needed to apply it are often too restrictive. We provide a further generalization 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 $A_{2} (2)$ .

Keywords

Runge's method, integral points on varieties, abelian varieties

Mathematical Subject Classification 2010

Primary: 11G35

Secondary: 11G10, 14G05, 14G35

Supplementary material

Sage_Algorithm

Milestones

Received: 8 January 2018

Revised: 30 August 2018

Accepted: 8 October 2018

Published: 13 February 2019

Authors

Samuel Le Fourn
University of Warwick Coventry CV5 6EF United Kingdom

Vol. 13, No. 1, 2019