Arithmetic of K3 surfaces

2008/08/07 by Matthias Schuett, Schuett, Matthias
Mathematics · #11F11 #11G15 #11G25 #14G05 #14G10 #14J28 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11F11 #msc:11G15 #msc:11G25 #msc:14G05 #msc:14G10 #msc:14J28

paper · pdf · doi:10.48550/arxiv.0808.1061

19 pages; v3: reference [5] added in section 13

openalex publication_date 2008/08/07 · arxiv created 2008/09/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We review recent developments in the arithmetic of K3 surfaces. Our focus lies on aspects of modularity, Picard number and rational points. Throughout we emphasise connections to geometry.

Citations

• Three lectures on elliptic surfaces and curves of high rank
• Modular Elliptic Curves and Fermat's Last Theorem

Related

• Two lectures on the arithmetic of K3 surfaces
• K3 surfaces with Picard number one and infinitely many rational points
• Point counting on K3 surfaces and an application concerning real and complex multiplication
• Counting rational curves on K3 surfaces
• Fields of definition of singular K3 surfaces