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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2601.13277 |
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| _version_ | 1866911386544635904 |
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| author | Bernasconi, Fabio Martin, Gebhard Patakfalvi, Zsolt |
| author_facet | Bernasconi, Fabio Martin, Gebhard Patakfalvi, Zsolt |
| contents | In this expository article, we prove a birational classification of smooth projective models of surfaces with negative Kodaira dimension over $\mathbb{Z}$ and over more general rings of integers $\mathcal{O}_K$, depending on their arithmetic and cohomological invariants. Along the way we collect some results on smooth projective models of surfaces over Dedekind domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13277 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On surfaces with smooth projective models over $\mathbb{Z}$ Bernasconi, Fabio Martin, Gebhard Patakfalvi, Zsolt Algebraic Geometry In this expository article, we prove a birational classification of smooth projective models of surfaces with negative Kodaira dimension over $\mathbb{Z}$ and over more general rings of integers $\mathcal{O}_K$, depending on their arithmetic and cohomological invariants. Along the way we collect some results on smooth projective models of surfaces over Dedekind domains. |
| title | On surfaces with smooth projective models over $\mathbb{Z}$ |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2601.13277 |