  Inspired by recent work of Farb, Kisin and Wolfson, we develop a method for
using actions of finite group schemes over a mixed characteristic dvr R to get
lower bounds for the essential dimension of a cover of a variety over K =
Frac(R). We then apply this to prove p-incompressibility for congruence covers
of a class of unitary Shimura varieties for primes p at which the reduction of
the Shimura variety (at any prime of the reflex field over p) does not have any
ordinary points. We also make some progress towards a conjecture of Brosnan on
the p-incompressibility of the multiplication by p map of an abelian variety.
