  The crystalline period map is a tool for linearizing $p$-divisible groups. It
has been applied to study the Langlands correspondences, and has possible
applications to the homotopy groups of spheres. The original construction of
the period map is inherently local. We present an alternative construction,
giving a map on the entire moduli stack of $p$-divisbile groups, up to isogeny,
which specializes to the original local construction.
