Moduli spaces of abelian varieties with Iwahori level structure
Seminar Room 1, Newton Institute
We discuss moduli spaces of abelian varieties in positive characteristic $p$, with Iwahori level structure at $p$. In contrast to the moduli space of principally polarized abelian varieties these spaces are singular and are considerably more complicated.
Their local structure can be described quite explicitly in terms of matrix equations. As to the global structure, the most interesting part is the supersingular locus (in other words the unique closed "Newton stratum"), whose structure is closely related to Deligne-Lusztig varieties.