On the section conjecture over fields of finite type
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Wiley Open Access
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| Format: | Artículo Open Access |
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Wiley
2025
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| _version_ | 1867021998596554752 |
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| author | Giulio Bresciani |
| author_facet | Giulio Bresciani Giulio Bresciani |
| collection | Wiley Open Access |
| contents | On the section conjecture over fields of finite type Giulio Bresciani Mathematische Nachrichten Abstract Assume that the section conjecture holds over number fields. We prove then that it holds for a broad class of curves defined over finitely generated extensions of . This class contains every projective, hyperelliptic curve, every hyperbolic, affine curve of genus , and a basis of open subsets of any curve. If we furthermore assume the weak Bombieri–Lang conjecture, we prove that the section conjecture holds for every hyperbolic curve over every finitely generated extension of . 10.1002/mana.70049 http://creativecommons.org/licenses/by/4.0/ |
| doi_str_mv | 10.1002/mana.70049 |
| format | Artículo Open Access |
| id | wiley_oa_10_1002_mana_70049 |
| institution | Wiley Open Access |
| license_str_mv | http://creativecommons.org/licenses/by/4.0/ |
| publishDate | 2025 |
| publisher | Wiley |
| record_format | wiley_oa |
| spellingShingle | On the section conjecture over fields of finite type Giulio Bresciani Mathematische Nachrichten On the section conjecture over fields of finite type Giulio Bresciani Mathematische Nachrichten Abstract Assume that the section conjecture holds over number fields. We prove then that it holds for a broad class of curves defined over finitely generated extensions of . This class contains every projective, hyperelliptic curve, every hyperbolic, affine curve of genus , and a basis of open subsets of any curve. If we furthermore assume the weak Bombieri–Lang conjecture, we prove that the section conjecture holds for every hyperbolic curve over every finitely generated extension of . 10.1002/mana.70049 http://creativecommons.org/licenses/by/4.0/ |
| title | On the section conjecture over fields of finite type |
| topic | Mathematische Nachrichten |
| url | https://onlinelibrary.wiley.com/doi/10.1002/mana.70049 |