GHOST CLASSES IN THE COHOMOLOGY OF THE SHIMURA VARIETY ASSOCIATED TO GSp(4)

摘要

In this paper we study the existence of ghost classes in the cohomology of the Shimura variety associated to the group of symplectic similitudes GSp(4). The existence of ghost classes for the trivial coefficient system is known. We show that ghost classes only exist for the trivial coefficient system and they lie in the cohomology group in degree 2. Moreover we prove that the weight of the mixed Hodge structure associated to the space of ghost classes is the middle weight.