Intersections of Hecke correspondences on modular curves
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908247160520704 |
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| author | He, Qiao Zhu, Baiqing |
| author_facet | He, Qiao Zhu, Baiqing |
| contents | We compute the arithmetic intersections of Hecke correspondences on the product of integral model of modular curve $\mathcal{X}_0(N)$ and relate it to the derivatives of certain Siegel Eisenstein series when $N$ is odd and squarefree. We prove this by establishing a precise identity between the arithmetic intersection numbers on the Rapoport--Zink space associated to $\mathcal{X}_0(N)^{2}$ and the derivatives of local representation densities of quadratic forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19600 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intersections of Hecke correspondences on modular curves He, Qiao Zhu, Baiqing Number Theory Algebraic Geometry We compute the arithmetic intersections of Hecke correspondences on the product of integral model of modular curve $\mathcal{X}_0(N)$ and relate it to the derivatives of certain Siegel Eisenstein series when $N$ is odd and squarefree. We prove this by establishing a precise identity between the arithmetic intersection numbers on the Rapoport--Zink space associated to $\mathcal{X}_0(N)^{2}$ and the derivatives of local representation densities of quadratic forms. |
| title | Intersections of Hecke correspondences on modular curves |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2502.19600 |