Alcoves et p-rang des vari\'et\'es ab\'eliennes
B. C. Ng\^o (IHES et CNRS Paris-Nord), A. Genestier (CNRS Paris-Sud)

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 -rank of abelian varieties in characteristic and the Kottwitz-Rapoport's stratification of the special fiber modulo of the moduli space of principally polarized abelian varieties with Iwahori type level structure on . In particular, the density of the ordinary locus in that special fiber is proved.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Meromorphic and Entire Functions · Advanced Algebra and Geometry
