Construction of Curves with a Controlled First Slope using p-Symmetric Numbers
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909040685088768 |
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| author | Moore, Robert Zhu, Hui June |
| author_facet | Moore, Robert Zhu, Hui June |
| contents | This paper establishes a constructive link between the first slope of Artin-Schreier curves X_f: y^p-y=f(x) and the p-adic weight of the support of f(x). If the maximal p-adic weight element v in Supp(f) is unique, we show that the first slope's lower bound of 1/s_p(v) is achieved if and only if v satisfies a combinatorial p-adic condition, which we define as p-symmetry. As an application, we construct explicit families of curves in every characteristic p with first slope equal to 1/n for every n>2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01832 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Construction of Curves with a Controlled First Slope using p-Symmetric Numbers Moore, Robert Zhu, Hui June Algebraic Geometry Number Theory This paper establishes a constructive link between the first slope of Artin-Schreier curves X_f: y^p-y=f(x) and the p-adic weight of the support of f(x). If the maximal p-adic weight element v in Supp(f) is unique, we show that the first slope's lower bound of 1/s_p(v) is achieved if and only if v satisfies a combinatorial p-adic condition, which we define as p-symmetry. As an application, we construct explicit families of curves in every characteristic p with first slope equal to 1/n for every n>2. |
| title | Construction of Curves with a Controlled First Slope using p-Symmetric Numbers |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2411.01832 |