On the representability of moduli problems on Hilbert moduli stacks

Abstract: It is often fundamental for the study of a moduli space to know whether the underlying moduli problem is representable. In the first part of this talk we discuss explicit representability criteria for moduli problems on the Hilbert moduli stacks of Rapoport and Deligne-Pappas. Our criteria also apply over the bad primes and they are optimal in many situations of interest. In the second part, we consider applications of our criteria to the study of integral points on Hilbert modular varieties and we explain how the work of Masser-Wustholz is used in the proofs. This is joint work with Arno Kret.