Is there a standard meaning for ordinary and supersingular Abelian varieties over finite fields? If so, where can I find it (together with basic properties about them)?
See http://en.wikipedia.org/wiki/Hasse-Witt_matrix#Abelian_varieties_and_their_p-rank . "Ordinary" is always defined by p-rank equal to the dimension (the maximum possible). The article gives one definition of "supersingular", but that usage may not be universal.