Bounding integral points on the Siegel modular variety A2(2)
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 A2(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.
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