Special lifts of ordinary K3 surfaces and applications

2006/11/15 by Jeng-Daw Yu, Yu, Jeng-Daw
Arts and Humanities · Mathematics · #14J28 (Primary) 14C25 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Historical Studies and Socio-cultural Analysis

paper · pdf · doi:10.48550/arxiv.math/0611481

openalex publication_date 2006/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the cohomological properties of quasi-canonical lifts of an ordinary K3 surface over a finite field. As applications, we prove a Torelli type theorem for ordinary K3 surfaces over finite fields and establish the Hodge conjecture for arbitrary self products of certain K3 surfaces over the complex numbers.

Related

• CM liftings of K3 surfaces over finite fields and their applications to the Tate conjecture
• K3 surfaces of finite height over finite fields
• Construction of quasi-canonical liftings of K3 surfaces of finite height in odd characteristic
• The Hodge standard conjecture for self-products of K3 surfaces
• Ordinary K3 surfaces over a finite field