  We study the formal neighbourhood of a point in $\mu$-ordinary locus of an
integral model of a Hodge type Shimura variety. We show that this formal
neighbourhood has a structure of a shifted cascade. Moreover we show that the
CM points on the formal neighbourhood are dense and that the identity section
of the shifted cascade corresponds to a lift of the abelian variety which has a
characterization in terms of its endomorphisms in analogy with the Serre-Tate
canonical lift of an ordinary abelian variety.
