Point counting on $K3$ surfaces and an application concerning real and   complex multiplication
  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. 
Andreas-Stephan Elsenhans and J\"org Jahnel
math.NT math.AG