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  Ghost classes in Q-rank two orthogonal Shimura varieties

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.

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Latex : Ghost classes in $\mathbb{Q}$-rank two orthogonal Shimura varieties

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Bajpai-Moya Giusti_Ghost classes in Q-rank two orthogonal Shimura varieties_2020.pdf (Publisher version), 364KB
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Bajpai-Moya Giusti_Ghost classes in Q-rank two orthogonal Shimura varieties_2020.pdf
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This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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https://doi.org/10.1007/s00209-020-02460-5 (Publisher version)
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 Creators:
Bajpai, Jitendra1, Author           
Moya Giusti, Matias Victor1, Author           
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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 Abstract: 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.

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Language(s): eng - English
 Dates: 2020
 Publication Status: Issued
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 Rev. Type: Peer
 Identifiers: DOI: 10.1007/s00209-020-02460-5
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Title: Mathematische Zeitschrift
  Abbreviation : Math. Z.
Source Genre: Journal
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Publ. Info: Springer
Pages: - Volume / Issue: 296 (3-4) Sequence Number: - Start / End Page: 1209 - 1233 Identifier: -