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PreprintCC BY 4.0arXiv

On the arithmetic Siegel--Weil formula for orthogonal Shimura varieties over a general totally real field

  • Xuanyou Li
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Abstract

Let F/ℚp be a finite extension with p≠ 2, and let V be a quadratic space over F of dimension at least two admitting a self-dual lattice. We prove the local arithmetic Siegel-Weil formula for GSpin Rapoport-Zink spaces formulated by Li and Zhang. We use the global-to-local strategy of Mihatsch and Zhang and its application by Luo. Using a generalization of the prismatic realization functor of Imai, Kato, and Youcis, we construct and study derived special cycles on integral models of SO Shimura varieties and their Rapoport-Zink uniformizations. We derive the local intersection formula from the modularity of special cycles on the generic fiber. As a first application, we prove the corresponding semi-global arithmetic Siegel-Weil identity for orthogonal Shimura varieties over a totally real field F≠ℚ.

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Cite

BibTeXRIS
BibTeX
@misc{li2026arithmetic,
  title = {{On the arithmetic Siegel--Weil formula for orthogonal Shimura varieties over a general totally real field}},
  author = {Xuanyou Li},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31173},
  eprint = {2610.31173},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31173},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the arithmetic Siegel--Weil formula for orthogonal Shimura varieties over a general totally real field
AU  - Xuanyou Li
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31173
UR  - https://arxiv.org/abs/2610.31173
AB  - Let F/ℚ_p be a finite extension with p≠ 2, and let V be a quadratic space over F of dimension at least two admitting a self-dual lattice. We prove the local arithmetic Siegel-Weil formula for GSpin Rapoport-Zink spaces formulated by Li and Zhang. We use the global-to-local strategy of Mihatsch and Zhang and its application by Luo. Using a generalization of the prismatic realization functor of Imai, Kato, and Youcis, we construct and study derived special cycles on integral models of SO Shimura varieties and their Rapoport-Zink uniformizations. We derive the local intersection formula from the modularity of special cycles on the generic fiber. As a first application, we prove the corresponding semi-global arithmetic Siegel-Weil identity for orthogonal Shimura varieties over a totally real field F≠ℚ.
ER  -