Elevators for degenerations of PEL structures

We show that the maximal rank of mixed characteristic degenerations of abelian varieties parameterized by a PEL-type Shimura variety are the same as the maximal rank of equicharacteristic zero degenerations (of abelian varieties parameterized by the same Shimura variety). As a byproduct, we obtain a simple proof of Yasuo Morita's conjecture in 1975 that an abelian variety with additional structures parameterized by a compact PEL-type Shimura variety has potential good reductions everywhere.