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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.08033 |
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| _version_ | 1866915650270658560 |
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| author | Zhu, Ziyang |
| author_facet | Zhu, Ziyang |
| contents | In this paper, we presents a method for factoring morphisms between arithmetic surfaces based on the regularity of arithmetic surfaces. Using this factorization, we derive a Riemann-Hurwitz formula satisfied by the ramification divisor and the canonical divisor on arithmetic surfaces. We also extend this formula to Arakelov theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08033 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Riemann-Hurwitz Formula for Arithmetic Surfaces Zhu, Ziyang Algebraic Geometry 14G40 In this paper, we presents a method for factoring morphisms between arithmetic surfaces based on the regularity of arithmetic surfaces. Using this factorization, we derive a Riemann-Hurwitz formula satisfied by the ramification divisor and the canonical divisor on arithmetic surfaces. We also extend this formula to Arakelov theory. |
| title | Riemann-Hurwitz Formula for Arithmetic Surfaces |
| topic | Algebraic Geometry 14G40 |
| url | https://arxiv.org/abs/2510.08033 |