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Proceedings of the American Mathematical Society

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


Author: Matias Victor Moya Giusti
Journal: Proc. Amer. Math. Soc. 146 (2018), 2315-2325
MSC (2010): Primary 14G35, 14D07
DOI: https://doi.org/10.1090/proc/13788
Published electronically: March 9, 2018
MathSciNet review: 3778137
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Abstract: 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.


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Additional Information

Matias Victor Moya Giusti
Affiliation: Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
Address at time of publication: CIEM-FaMAF, Universidad Nacional de Córdoba, Medina Allende s/n - Ciudad Universitaria, CP. 5016, Córdoba, Argentina
Email: moya@famaf.unc.edu.ar

DOI: https://doi.org/10.1090/proc/13788
Keywords: Shimura varieties, Ghost classes, Mixed Hodge structures
Received by editor(s): November 12, 2016
Received by editor(s) in revised form: March 21, 2017
Published electronically: March 9, 2018
Additional Notes: This paper is based on part of the author’s doctoral thesis at Université Paris Diderot - Paris 7, written under the direction of Michael Harris, where the author was supported by the ERC (European Research Council).
Communicated by: Romyar T. Sharifi
Article copyright: © Copyright 2018 American Mathematical Society