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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.04952 |
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| _version_ | 1866910730884743168 |
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| author | Niemann, Jonathan |
| author_facet | Niemann, Jonathan |
| contents | The classification of maximal function fields over a finite field is a difficult open problem, and even determining isomorphism classes among known function fields is challenging in general. We study a particular family of maximal function fields defined over a finite field with $q^2$ elements, where $q$ is the power of an odd prime. When $d := (q+1)/2$ is a prime, this family is known to contain a large number of non-isomorphic function fields of the same genus and with the same automorphism group. We compute the automorphism group and isomorphism classes also in the case where $d$ is not a prime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04952 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-isomorphic maximal function fields of genus $q-1$ Niemann, Jonathan Number Theory Algebraic Geometry 11G, 14G The classification of maximal function fields over a finite field is a difficult open problem, and even determining isomorphism classes among known function fields is challenging in general. We study a particular family of maximal function fields defined over a finite field with $q^2$ elements, where $q$ is the power of an odd prime. When $d := (q+1)/2$ is a prime, this family is known to contain a large number of non-isomorphic function fields of the same genus and with the same automorphism group. We compute the automorphism group and isomorphism classes also in the case where $d$ is not a prime. |
| title | Non-isomorphic maximal function fields of genus $q-1$ |
| topic | Number Theory Algebraic Geometry 11G, 14G |
| url | https://arxiv.org/abs/2412.04952 |