Point counting on K3 surfaces and an application concerning real and complex multiplication

2016/02/13 by Elsenhans, Andreas-Stephan, Jahnel, Jörg
#11G15 #11M38 (secondary) #11Y16 #14J28 (primary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1602.04327

Abstract

We report on our project to find explicit examples of K3 surfaces having real or complex multiplication. Our strategy is to search through the arithmetic consequences of RM and CM. In order to do this, an efficient method is needed for point counting on surfaces defined over finite fields. For this, we describe algorithms that are p-adic in nature.

Related

• 2-adic point counting on K3 surfaces
• Arithmetic of K3 surfaces
• K3 surfaces with real or complex multiplication
• Explicit families of K3 surfaces having real multiplication
• Real and complex multiplication on K3 surfaces via period integration