On distribution of supersingular primes of abelian varieties and K3 surfaces

Let K be a global field and let X/K be a non-CM abelian variety or non-CM K3 surface. We prove that the density of the supersingular primes of X is zero. When K is a number field, we obtain asymptotic upper bounds of the counting function for supersingular primes by applying the effective Chebotarev density theorem for infinite Galois extensions due to Serre.