p-rank (reviewed)

Let $A$ be a $g$-dimensional abelian variety over $\F_q$ where $q=p^r$. The $p$-rank of $A$ is the dimension of the geometric $p$-torsion as an $\F_p$-vector space: $$p\operatorname{-rank}(A) = \dim_{\F_p}( A(\overline{\F}_p)[p] ).$$ The $p$-rank is at most $g$, with equality if and only if $A$ is ordinary. The difference between $g$ and the $p$-rank is the $p$-rank deficit of $A$.