In a recent article, Farb, Kisin and Wolfson proved that principal
p-congruence covers of Siegel modular varieties (and certain subvarieties
thereof) are incompressible, i.e., are not (rationally) the base change of covers
of lower dimensional varieties. In joint work with Patrick Brosnan we
found a different proof, which also applies to some exceptional Shimura
varieties, and our results suggest that incompressibility should hold for
all Shimura varieties and almost all primes p. In my talk I will discuss the
case of p-congruence covers of some unitary Shimura varieties for primes
p at which the special fibre of Kottwitz's integral model has no ordinary points.
(Based on joint work with Rijul Saini.)
