The unpolarized Shafarevich Conjecture for K3 Surfaces

TL;DR

This paper proves the unpolarized Shafarevich conjecture for K3 surfaces, establishing finiteness of isomorphism classes over a number field with controlled reduction, using advanced theorems and the Kuga-Satake construction.

Contribution

It provides a proof of the conjecture for K3 surfaces, extending the understanding of their arithmetic properties over number fields.

Findings

Finiteness of K3 surfaces over fixed number fields with specified reduction.

Application of Faltings and André's theorems to K3 surfaces.

Utilization of the Kuga-Satake construction in the proof.

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.