The unpolarized Shafarevich Conjecture for K3 Surfaces (1705.09038v1)

Abstract: We prove the unpolarized Shafarevich conjecture for K3 surfaces: the set of isomorphism classes of K3 surfaces over a fixed number field with good reduction away from a fixed and finite set of places is finite. Our proof is based on the theorems of Faltings and Andr\'e, as well as the Kuga-Satake construction.