Points of low degree on curves over function fields
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914442949689344 |
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| author | van Schaick, Sièna |
| author_facet | van Schaick, Sièna |
| contents | We show that the geometric classification of smooth projective curves admitting infinitely many points of degree $d\leq 5$ extends from number fields to function fields of characteristic 0. Over number fields, this classification was established by Faltings for $d=1$, Harris--Silverman for $d=2$, Abramovich--Harris for $d=3,4$ and Kadets--Vogt for $d=4,5$. Our approach uses a specialization argument to reduce the problem over function fields to the number field case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02975 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Points of low degree on curves over function fields van Schaick, Sièna Number Theory Algebraic Geometry 14G99 (Primary) 11G30, 14H45, 14G05 (Secondary) We show that the geometric classification of smooth projective curves admitting infinitely many points of degree $d\leq 5$ extends from number fields to function fields of characteristic 0. Over number fields, this classification was established by Faltings for $d=1$, Harris--Silverman for $d=2$, Abramovich--Harris for $d=3,4$ and Kadets--Vogt for $d=4,5$. Our approach uses a specialization argument to reduce the problem over function fields to the number field case. |
| title | Points of low degree on curves over function fields |
| topic | Number Theory Algebraic Geometry 14G99 (Primary) 11G30, 14H45, 14G05 (Secondary) |
| url | https://arxiv.org/abs/2604.02975 |