The unpolarized Shafarevich Conjecture for K3 Surfaces

2017/05/25 by Yiwei She, She, Yiwei · 6 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Combinatorics #Computer science #Conjecture #Crystallography #Discrete mathematics #FOS: Mathematics #Field (mathematics) #Finite field #Finite set #Geometry #Good reduction #Isomorphism (crystallography) #Mathematical analysis #Mathematics #Number Theory (math.NT) #Programming language #Pure mathematics #Reduction (mathematics) #Set (abstract data type) #math.NT

paper · pdf · doi:10.48550/arxiv.1705.09038

published in arXiv (Cornell University) (Cornell University)

arxiv created 2017/05/25 · openalex publication_date 2017/05/25 · arxiv updated 2017/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

• On the Shafarevich conjecture for Enriques surfaces
• Finiteness of pointed families of symplectic varieties: a geometric Shafarevich conjecture

Related

• Unpolarized Shafarevich conjectures for hyper-Kähler varieties
• Unpolarized Shafarevich conjectures for hyper-Kähler varieties
• On the Shafarevich conjecture for Enriques surfaces
• Neighbors and arithmetic of isogenous K3 surfaces
• Ample Divisors, Automorphic Forms and Shafarevich's Conjecture