  We first recall Grothendieck's notion of n-truncated Barsotti-Tate group.
Such groups form an algebraic stack over the integers. The problem is to give
an illuminating description of its reductions modulo powers of p. A related
problem is to construct analogs of these reductions related to general Shimura
varieties with good reduction at p. We discuss some conjectures on this subject
based on the theory of prismatic cohomology.
