Sustained $p$-divisible groups

In 1999 Frans Oort introduced the notion of "geometrically fiberwise constant $p$-divisible groups" and used it to define (central) leaves in moduli spaces of abelian varieties with additional structures in characteristic $p>0$. This is a "pointwise" definition, in line with the definition of many natural stratification structure on moduli spaces.

In this talk we will report a notion of "sustained $p$-divisible groups" over general base schemes in characteristic $p>0$ and its basic properties, obtained in joint work in progress with Oort. This newer definition coincides with the previous one when the base scheme is (noetherian and) reduced, and helps in studying differential properties of leaves.