Ghost classes in Q-rank two orthogonal Shimura varieties

Bajpai, Jitendra; Moya Giusti, Matias Victor

doi:10.1007/s00209-020-02460-5

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Ghost classes in Q-rank two orthogonal Shimura varieties

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Bajpai, Jitendra
Max Planck Institute for Mathematics, Max Planck Society;

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

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https://doi.org/10.1007/s00209-020-02460-5
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Bajpai-Moya Giusti_Ghost classes in Q-rank two orthogonal Shimura varieties_2020.pdf
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引用

Bajpai, J., & Moya Giusti, M. V. (2020). Ghost classes in Q-rank two orthogonal Shimura varieties. Mathematische Zeitschrift, 296(3-4), 1209-1233. doi:10.1007/s00209-020-02460-5.

引用: https://hdl.handle.net/21.11116/0000-0006-9C05-5

要旨

In this article, the existence of ghost classes for the Shimura varieties associated to algebraic
groups of orthogonal similitudes of signature (2, n) is investigated. We make use of the study of the weights in the mixed Hodge structures associated to the corresponding cohomology spaces and results on the Eisenstein cohomology of the algebraic group of orthogonal similitudes of signature (1, n −1). For the values of n = 4, 5 we prove the non-existence of ghost classes for most of the irreducible representations (including most of those with an irregular highest weight). For the rest of the cases, we prove strong restrictions on the possible weights in the space of ghost classes and, in particular, we show that they satisfy the weak middle weight property.