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Journal Article

On the existence of ghost classes in the cohomology of the Shimura variety associated to GU(2,2)

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Moya Giusti,  Matias Victor
Max Planck Institute for Mathematics, Max Planck Society;

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http://dx.doi.org/10.4310/MRL.2018.v25.n4.a9
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Citation

Moya Giusti, M. V. (2018). On the existence of ghost classes in the cohomology of the Shimura variety associated to GU(2,2). Mathematical Research Letters, 25(4), 1227-1249. doi:10.4310/MRL.2018.v25.n4.a9.


Cite as: https://hdl.handle.net/21.11116/0000-0003-ACDE-2
Abstract
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.