Counting abelian varieties over finite fields via Frobenius densities

Let $[X,\lambda]$ be a principally polarized abelian variety over finite field with commutative endomorphism ring; further suppose that either $X$ is ordinary or the prime. Motivated by an equidistribution heuristic, we introduce factor $\nu_v([X,\lambda])$ for each place $v$ of $\mathbb Q$, and show product these factors essentially computes size isogeny class $[X,\lambda]$. The derivation this mass formula depends on Kottwitz analysis measures group symplectic similitudes, in particular does not rely calculation numbers.