Modular Heights of Quaternionic Shimura Curves
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910459299364864 |
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| author | Yuan, Xinyi |
| author_facet | Yuan, Xinyi |
| contents | The goal of this paper is to prove a formula expressing the modular height of a quaternionic Shimura curve over a totally real number field in terms of the logarithmic derivative of the Dedekind zeta function of the totally real number field. Our proof is based on the work of Yuan-Zhang-Zhang on the Gross-Zagier formula and the work of Yuan-Zhang on the averaged Colmez conjecture. All these works are in turn inspired by the Pioneering work of Gross-Zagier and some philosophies of Kudla's program. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_13995 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Modular Heights of Quaternionic Shimura Curves Yuan, Xinyi Number Theory Algebraic Geometry 11G18, 11F67, 14G40 The goal of this paper is to prove a formula expressing the modular height of a quaternionic Shimura curve over a totally real number field in terms of the logarithmic derivative of the Dedekind zeta function of the totally real number field. Our proof is based on the work of Yuan-Zhang-Zhang on the Gross-Zagier formula and the work of Yuan-Zhang on the averaged Colmez conjecture. All these works are in turn inspired by the Pioneering work of Gross-Zagier and some philosophies of Kudla's program. |
| title | Modular Heights of Quaternionic Shimura Curves |
| topic | Number Theory Algebraic Geometry 11G18, 11F67, 14G40 |
| url | https://arxiv.org/abs/2205.13995 |