Cyclic Cubic Points on Higher Genus Curves
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866911201988968448 |
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| author | Rawson, James |
| author_facet | Rawson, James |
| contents | The distribution of degree $d$ points on curves is well understood, especially for low degrees. We refine this study to include information on the Galois group in the simplest interesting case: $d = 3$. For curves of genus at least 5, we show cubic points with Galois group $C_3$ arise from well-structured morphisms, along with providing computable tests for the existence of such morphisms. We prove the same for curves of lower genus under some geometric or arithmetic assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13743 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cyclic Cubic Points on Higher Genus Curves Rawson, James Number Theory 11G30, 11G35, 14G05, 14H25 The distribution of degree $d$ points on curves is well understood, especially for low degrees. We refine this study to include information on the Galois group in the simplest interesting case: $d = 3$. For curves of genus at least 5, we show cubic points with Galois group $C_3$ arise from well-structured morphisms, along with providing computable tests for the existence of such morphisms. We prove the same for curves of lower genus under some geometric or arithmetic assumptions. |
| title | Cyclic Cubic Points on Higher Genus Curves |
| topic | Number Theory 11G30, 11G35, 14G05, 14H25 |
| url | https://arxiv.org/abs/2405.13743 |