  Let k be a perfect field of characteristic p>0. We prove the existence of
ascending and descending slope filtrations for Shimura p-divisible objects over
k. We use them to classify rationally these objects over \bar k. Among
geometric applications, we mention two. First we formulate Manin problems for
Shimura varieties of Hodge type. We solve them if either p\Ge 3 or p=2 and two
mild conditions hold. Second we formulate integral Manin problems. We solve
them for certain Shimura varieties of PEL type.
