The unpolarized Shafarevich Conjecture for K3 Surfaces

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 André, as well as the Kuga-Satake construction.

Cited by in corpus (4)

• Finiteness theorems for K3 surfaces and abelian varieties of CM type
• The Shafarevich conjecture for hypersurfaces in abelian varieties
• On uniformity conjectures for abelian varieties and K3 surfaces
• On the Shafarevich conjecture for Enriques surfaces