  We study the rigid cohomology of the ordinary locus in some compact PEL
Shimura varieties of type C with values in automorphic local systems and use it
to prove a small slope criterion for classicality of overconvergent Hecke
eigenforms. This generalises the work of Coleman, and is a first step in an
ongoing project to extend the cohomological approach to classicality to
higher-dimensional Shimura varieties.
