Ghost classes in the cohomology of the Shimura variety associated to GSp_4

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...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2018-06, Vol.146 (6), p.2315-2325
Main Author: Moya Giusti, Matias Victor
Format: Article
Language:English
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Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/13788