On specializations of minimal $p$-divisible groups

Abstract

In this paper, for any pair $(\zeta, \xi)$ of Newton polygons with $\zeta \prec \xi$, we construct a concrete specialization from the minimal $p$-divisible group of $\xi$ to the minimal $p$-divisible group of $\zeta$ by a beautiful induction. This in particular gives the affirmative answer to the unpolarized analogue of a question by Oort on the boundaries of central streams, and gives another proof of the dimension formula of the central leaves in the unpolarized case.