Serre and Tate defined "canonical coordinates" locally around the moduli point of a polarized ordinary abelian variety. In this talk we will describe two kind of generalizations (joint work with Ching-Li Chai): -- describe global coordinates; -- describe a generalization to the non-ordinary case. For the last we need the notion of a foliation. We will describe this, and give properties and examples. Then we describe the proof with the help of a new notion about p-divisible groups over an arbitrary base scheme.