EXISTENCE OF GEOMETRICALLY SIMPLE ORDINARY ABELIAN VARIETIES OVER A FIXED FINITE FIELD

HUI ZHU

Abstract. Given a prime number p and a positive integer d, we prove that there exist geometrically simple d-dimensional ordinary abelian varieties defined over the finite field of p elements. We present an algorithm to determine whether an abelian variety over a finite field k, given with the characteristic polynomial of its Frobenius endomorphism relative to k, is geometrically simple.