A note on Diophantine subsets of large fields
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916468813201408 |
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| author | Kwon, Andrew |
| author_facet | Kwon, Andrew |
| contents | Large fields (also called ample, anti-mordellic) generalize many fields of classical interest, such as algebraically closed fields, real-closed fields, and $p$-adic fields. In this note we answer a question of Pop by generalizing a result of Fehm and prove that finite unions of affine translates of infinite proper subfields are never diophantine subsets of perfect large fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03212 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on Diophantine subsets of large fields Kwon, Andrew Number Theory Algebraic Geometry Logic 12E30, 14G05, 12F99, 03C60 Large fields (also called ample, anti-mordellic) generalize many fields of classical interest, such as algebraically closed fields, real-closed fields, and $p$-adic fields. In this note we answer a question of Pop by generalizing a result of Fehm and prove that finite unions of affine translates of infinite proper subfields are never diophantine subsets of perfect large fields. |
| title | A note on Diophantine subsets of large fields |
| topic | Number Theory Algebraic Geometry Logic 12E30, 14G05, 12F99, 03C60 |
| url | https://arxiv.org/abs/2411.03212 |