Integral Points on Moduli Schemes and Siegel’s Theorem

Abstract: In this talk we give explicit finiteness results for integral points on moduli schemes of elliptic curves. After considering the general case, we focus on the so-called ‘moduli affine models’ of an arbitrary smooth projective curve defined over a number field and we discuss explicit versions of Siegel’s theorem for these affine models. We also explain the strategy of proof which combines the theory of logarithmic forms with the moduli formalism and constructions coming from anabelian geometry.