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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2606.01310 |
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| _version_ | 1866917552696852480 |
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| author | Knaf, Hagen Kuhlmann, Franz-Viktor |
| author_facet | Knaf, Hagen Kuhlmann, Franz-Viktor |
| contents | For an algebraic function field $F$ over a large field $K$, we show: 1) if $F|K$ has a rational place, then there is a finite purely inseparable extension $K'|K$ such that $K'$ is existentially closed in $F.K'$; 2) $F|K$ has a rational place admitting local uniformization if and only if $K$ is existentially closed in $F$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_01310 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Large imperfect fields are existentially closed in function fields after finite constant extension Knaf, Hagen Kuhlmann, Franz-Viktor Commutative Algebra Logic Primary 12J20, 12L12, secondary 12F20, 12J25, 14H05 For an algebraic function field $F$ over a large field $K$, we show: 1) if $F|K$ has a rational place, then there is a finite purely inseparable extension $K'|K$ such that $K'$ is existentially closed in $F.K'$; 2) $F|K$ has a rational place admitting local uniformization if and only if $K$ is existentially closed in $F$. |
| title | Large imperfect fields are existentially closed in function fields after finite constant extension |
| topic | Commutative Algebra Logic Primary 12J20, 12L12, secondary 12F20, 12J25, 14H05 |
| url | https://arxiv.org/abs/2606.01310 |