On distribution of supersingular primes of abelian varieties and K3 surfaces

Let X be an abelian variety or a K3 surface defined over a number field K. We prove that the density of the supersingular primes of X is zero if X is non-CM. By applying an effective Chebotarev density theorem of Serre, we obtain asymptotic upper bounds of the counting function for these supersingular primes.