Modular Heights of Unitary Shimura Varieties
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914063973351424 |
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| author | Guo, Ziqi |
| author_facet | Guo, Ziqi |
| contents | The goal of this paper is to prove a formula expressing the modular height of a unitary Shimura variety over a CM number field in terms of the logarithm derivative of the Hecke L-function associated with the CM extension. In a more specific term, we will introduce a global canonical integral model of such a unitary Shimura variety, and compute the arithmetic top self-intersection number of a canonical arithmetic line bundle with Hermitian metric on such integral model. At the same time, we also delve into a thorough investigation of the arithmetic generating series of divisors on unitary Shimura varieties. Therefore, we will also obtain the so-called ``arithmetic Siegel-Weil formula'' in our setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24363 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modular Heights of Unitary Shimura Varieties Guo, Ziqi Number Theory 11G40 11G50 14G10 14G35 14G40 The goal of this paper is to prove a formula expressing the modular height of a unitary Shimura variety over a CM number field in terms of the logarithm derivative of the Hecke L-function associated with the CM extension. In a more specific term, we will introduce a global canonical integral model of such a unitary Shimura variety, and compute the arithmetic top self-intersection number of a canonical arithmetic line bundle with Hermitian metric on such integral model. At the same time, we also delve into a thorough investigation of the arithmetic generating series of divisors on unitary Shimura varieties. Therefore, we will also obtain the so-called ``arithmetic Siegel-Weil formula'' in our setting. |
| title | Modular Heights of Unitary Shimura Varieties |
| topic | Number Theory 11G40 11G50 14G10 14G35 14G40 |
| url | https://arxiv.org/abs/2509.24363 |