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Lefschetz trace formula and \(\ell \)-adic cohomology of Rapoport–Zink tower for GSp(4)

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Abstract

We investigate the alternating sum of the \(\ell \)-adic cohomology of the Rapoport–Zink tower for GSp(4) by the Lefschetz trace formula. We observe that the local Jacquet–Langlands correspondence between GSp(4) and its inner form appears in the cohomology.

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Acknowledgements

The author would like to thank Tetsushi Ito and Matthias Strauch for valuable discussions. He is also grateful to Takuya Konno for helpful comments. This work was supported by JSPS KAKENHI Grant Numbers 21740022, 24740019.

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  1. Graduate School of Mathematical Sciences, The University of Tokyo, 3–8–1 Komaba, Meguro-ku, Tokyo, 153–8914, Japan

    Yoichi Mieda

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  1. Yoichi Mieda
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Correspondence to Yoichi Mieda.

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Communicated by Toby Gee.

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Mieda, Y. Lefschetz trace formula and \(\ell \)-adic cohomology of Rapoport–Zink tower for GSp(4). Math. Ann. 385, 131–192 (2023). https://doi.org/10.1007/s00208-021-02342-z

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  • DOI: https://doi.org/10.1007/s00208-021-02342-z

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