Abstract
We show a degree formula for a type of orthogonal Deligne–Lusztig varieties and their Plücker embeddings. This is an analog of work of Li on a unitary case.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data avaliability
Data sharing not applicable to this article as no datasets were generated or analysed during the current study.
References
Deligne, P., Lusztig, G.: Representations of reductive groups over finite fields. Ann. Math. (2) 103(1), 103–161 (1976). https://doi.org/10.2307/1971021
Li, C.: Degrees of unitary Deligne–Lusztig varieties (2023). arXiv:2301.08886v1
Li, C., Zhang, W.: Kudla–Rapoport cycles and derivatives of local densities. J. Am. Math. Soc. 35(3), 705–797 (2022). https://doi.org/10.1090/jams/988
Vollaard, I., Wedhorn, T.: The supersingular locus of the Shimura variety of \({\rm GU}(1, n-1)\) II. Invent. Math. 184(3), 591–627 (2011). https://doi.org/10.1007/s00222-010-0299-y
Howard, B., Pappas, G.: On the supersingular locus of the \({\rm GU}(2,2)\) Shimura variety. Algebra Number Theory 8(7), 1659–1699 (2014). https://doi.org/10.2140/ant.2014.8.1659
Li, C., Zhang, W.: On the arithmetic Siegel-Weil formula for GSpin Shimura varieties. Invent. Math. 228(3), 1353–1460 (2022). https://doi.org/10.1007/s00222-022-01106-z
Li, C., Liu, Y.: Chow groups and \(L\)-derivatives of automorphic motives for unitary groups, II. Forum Math. Pi 10, 5–71 (2022). https://doi.org/10.1017/fmp.2022.2
Pless, V.: The number of isotropic subspaces in a finite geometry. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 39, 418–421 (1965)
Acknowledgements
The author thanks his previous adviser N. Imai for academically supporting him throughout this project. He also thanks C. Li for a conversation regarding this work and the referee for their suggestions to improve his writings. This work was supported by the Grant-in-Aid for JSPS fellows. (JSPS KAKENHI Grant No. 23KJ0750)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The author asserts that there are no conflicts of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Nakayama, Y. Degrees of some orthogonal Deligne–Lusztig varieties. Res. number theory 10, 34 (2024). https://doi.org/10.1007/s40993-024-00521-w
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40993-024-00521-w