Mathematical Research Letters
Volume 25 (2018)
On the existence of ghost classes in the cohomology of the Shimura variety associated to $GU(2, 2)$
Pages: 1227 – 1249
In this paper we study the existence of ghost classes in the cohomology of the Shimura variety attached to the group of unitary similitudes of signature $(2, 2)$, denoted by $GU(2, 2)$. We use considerations on the weights of the mixed Hodge structures attached to the cohomology spaces involved in their definition. The non-existence of ghost classes is known in the cases in which the highest weight of the irreducible representation is regular. We prove that for most irreducible representations with irregular highest weight there are no ghost classes and for the other cases we show that the possible weights in the mixed Hodge structure on the space of ghost classes belong always to the set consisting of the middle weight and the middle weight plus one.
Shimura varieties, ghost classes, mixed Hodge structures
2010 Mathematics Subject Classification
Received 17 June 2016