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

Samuel Le Fourn

Published 2016-11-28Version 1

Runge's method is a tool to figure out integral points on some curves, effectively in terms of height. This method has been generalised to varieties of any dimension, 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 a totally explicit finiteness result for integral points on the Siegel modular variety $A_2(2)$.