Liftability of Mod p Cusp Forms of Parallel Weights

We present a vanishing theorem for automorphic line bundles on good reduction fibers of PEL-type Shimura varieties (including all noncompact ones). As a consequence, we deduce that for a good prime p no smaller than the dimension of a PEL-type Shimura variety, any mod p cusp form of positive cohomological parallel weight is liftable to characteristic zero.