Classical Serre-Tate theory concerns the deformation theory of ordinary abelian varieties.  It implies that their deformation spaces can be equipped with a group structure and a lifting of the Frobenius morphism, and consequently such varieties admit a canonical lifting to characteristic zero.  In the talk, I will show how to obtain similar results for ordinary Calabi-Yau varieties of arbitrary dimension.  The main tools will be Frobenius splittings and a new construction of relative Witt vectors of length two. This is joint work with Maciej Zdanowicz (EPFL).