Alcoves et p-rang des vari\'et\'es ab\'eliennes

We study the relation between the $p$-rank of abelian varieties in characteristic $p$ and the Kottwitz-Rapoport’s stratification of the special fiber modulo $p$ of the moduli space of principally polarized abelian varieties with Iwahori type level structure on $p$. In particular, the density of the ordinary locus in that special fiber is proved.