The supersingular locus in Siegel modular varieties with Iwahori level structure

Details The supersingular locus in Siegel modular varieties with Iwahori level structure The supersingular locus in Siegel modular varieties with Iwahori level structure

2008-07-08

arxiv.org/abs/0807.1229v3

Mathematics

Algebraic Geometry

v2: Expanded Section 3; minor changes. v3: Added several clarifications. 29 pages

Scientific paper

We study moduli spaces of abelian varieties in positive characteristic, more specifically the moduli space of principally polarized abelian varieties on the one hand, and the analogous space with Iwahori type level structure, on the other hand. We investigate the Ekedahl-Oort stratification on the former, the Kottwitz-Rapoport stratification on the latter, and their relationship. In this way, we obtain structural results about the supersingular locus in the case of Iwahori level structure, for instance a formula for its dimension in case $g$ is even.

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