Intersections of Hecke correspondences on the modular varieties of $\mathcal{D}$-elliptic sheaves
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910801526259712 |
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| author | Ülkem, Özge Wei, Fu-Tsun |
| author_facet | Ülkem, Özge Wei, Fu-Tsun |
| contents | This paper studies the intersections of Hecke correspondences on the modular varieties of $\mathcal{D}$ -elliptic sheaves in the higher-rank setting, where $\mathcal{D}$ is a "maximal order" in a central division algebra $D$ over a global function field $k$. Assuming that $\dim_k(D) = r^2$, where $r$ is a prime distinct from the characteristic of $k$, we express the intersection numbers of Hecke correspondences as suitable combinations of modified Hurwitz class numbers of "imaginary orders". This result establishes a higher-rank analogue of the classical class number relation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15746 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intersections of Hecke correspondences on the modular varieties of $\mathcal{D}$-elliptic sheaves Ülkem, Özge Wei, Fu-Tsun Number Theory 11R58, 11G18 This paper studies the intersections of Hecke correspondences on the modular varieties of $\mathcal{D}$ -elliptic sheaves in the higher-rank setting, where $\mathcal{D}$ is a "maximal order" in a central division algebra $D$ over a global function field $k$. Assuming that $\dim_k(D) = r^2$, where $r$ is a prime distinct from the characteristic of $k$, we express the intersection numbers of Hecke correspondences as suitable combinations of modified Hurwitz class numbers of "imaginary orders". This result establishes a higher-rank analogue of the classical class number relation. |
| title | Intersections of Hecke correspondences on the modular varieties of $\mathcal{D}$-elliptic sheaves |
| topic | Number Theory 11R58, 11G18 |
| url | https://arxiv.org/abs/2501.15746 |