Conjecture on the size of isogeny classes of abelian varieties over finite fields

Let $N(W)$ be the open Newton stratum of $\mathcal{A}_{g}$ consisting of all abelian varieties whose Newton polygon is $W$, and let $A$ be a principally polarized abelian variety in $\mathcal{A}_{g}$. The central leaf through $A$ is the locus in $N(W)$ of abelian varieties whose $p$-divisible group is isomorphic to $A[p^{\infty}]$. The isogeny leaf through $A$ is a maximal irreducible subscheme of $\mathcal{A}_{g}$ consisting of abelian varieties $A'$ in $N(W)$ such that $A'$ is isogenous to $A$ through an isogeny whose kernel is an iteration extension of the group scheme $\alpha_p$. Let $\dim(CL)$ and $\dim(IL)$ denote the dimensions of the central and isogeny leaves through $A$, respectively.

Conjecture on isogeny class sizes. We have

$$N(q^{n},A)=q^{n\left(\frac{\dim(CL)}{2}+\dim(IL)\right)+o(1)}.$$

This conjecture proposes a general asymptotic formula for the size of the isogeny class of a principally polarized abelian variety over finite fields, in terms of the dimensions of its central and isogeny leaves. Its resolution status is not specified in the supplied text.