# Sur la m\'ethode de Runge et les points entiers de certaines vari\'et\'es modulaires de Siegel

## TL;DR

This paper extends Runge's method to higher dimensions to study integral points on certain modular varieties, providing explicit results for the Siegel modular variety A_2(2).

## Contribution

It generalizes Runge's method to higher dimensions and applies it to obtain explicit results on integral points for specific Siegel modular varieties.

## Key findings

- Explicit description of integral points on A_2(2).
- Generalization of Runge's method to higher-dimensional varieties.
- New bounds for integral points on certain modular varieties.

## Abstract

In this note, we announce results on integral points on some modular varieties, based on a generalisation of Runge's method in higher dimensions which will be explained beforehand. In particular, we obtain an explicit result in the case of the Siegel modular variety $A_2(2)$.