Bounding integral points on the Siegel modular variety A_2(2)
Number Theory
2021-03-08 v2
Abstract
We determine two explicit upper bounds for the stable Faltings height of principally polarised abelian surfaces over number fields corresponding to S-integral points on the Siegel modular variety A_2(2). One upper bound, using Runge's method, is uniform in S as long as |S|<3; the other, using Baker's method, is not uniform but allows |S|<10. Our application of a higher-dimensional Baker's method is completely explicit and improves upon the general case due to Levin.
Cite
@article{arxiv.2007.14422,
title = {Bounding integral points on the Siegel modular variety A_2(2)},
author = {Josha Box and Samuel le Fourn},
journal= {arXiv preprint arXiv:2007.14422},
year = {2021}
}
Comments
See https://github.com/joshabox/IntegralpointsonA22 for the complementary Magma code