Point counting on K3 surfaces and an application concerning real and complex multiplication
Andreas-Stephan Elsenhans, Jörg Jahnel · LMS Journal of Computation and Mathematics · 2016
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.