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

TL;DR

This paper investigates the relationship between the p-rank of abelian varieties in characteristic p and the stratification of their moduli space, proving the density of the ordinary locus in the special fiber.

Contribution

It establishes a connection between p-rank and Kottwitz-Rapoport stratification, proving the density of the ordinary locus in the moduli space's special fiber.

Findings

Density of the ordinary locus in the special fiber is proved

Relation between p-rank and stratification is clarified

Insights into the structure of moduli spaces in characteristic p

Abstract

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.