Integral points on coarse Hilbert moduli schemes

Abstract: I will present explicit bounds for the height and the number of integral points on coarse Hilbert moduli schemes outside the branch locus. Furthermore, I will illustrate the results with examples given by certain classical surfaces and I will explain the strategy of proof which combines the method of Faltings (Arakelov, Parsin, Szpiro) with modularity and Masser Wustholz isogeny estimates. This is joint work with Arno Kret.