Abstract divisorial spaces and arithmetic intersection numbers
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914568104574976 |
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| author | Cai, Yulin Gubler, Walter |
| author_facet | Cai, Yulin Gubler, Walter |
| contents | Yuan and Zhang introduced arithmetic intersection numbers for adelic line bundles on quasi-projective varieties over a number field. Burgos and Kramer generalized this approach allowing more singular metrics at archimedean places. We introduce abstract divisorial spaces as a tool to generalize these arithmetic intersection numbers to the setting of a proper adelic base curve in the sense of Chen and Moriwaki. We also allow more singular metrics at non-archimedean places using relative mixed energy there as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00611 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Abstract divisorial spaces and arithmetic intersection numbers Cai, Yulin Gubler, Walter Algebraic Geometry Number Theory Primary 14G40, Secondary 11G50 Yuan and Zhang introduced arithmetic intersection numbers for adelic line bundles on quasi-projective varieties over a number field. Burgos and Kramer generalized this approach allowing more singular metrics at archimedean places. We introduce abstract divisorial spaces as a tool to generalize these arithmetic intersection numbers to the setting of a proper adelic base curve in the sense of Chen and Moriwaki. We also allow more singular metrics at non-archimedean places using relative mixed energy there as well. |
| title | Abstract divisorial spaces and arithmetic intersection numbers |
| topic | Algebraic Geometry Number Theory Primary 14G40, Secondary 11G50 |
| url | https://arxiv.org/abs/2409.00611 |