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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.14179 |
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| _version_ | 1866916217547128832 |
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| author | Beelen, Peter Montanucci, Maria Niemann, Jonathan Tilling Quoos, Luciane |
| author_facet | Beelen, Peter Montanucci, Maria Niemann, Jonathan Tilling Quoos, Luciane |
| contents | The problem of understanding whether two given function fields are isomorphic is well-known to be difficult, particularly when the aim is to prove that an isomorphism does not exist. In this paper we investigate a family of maximal function fields that arise as Galois subfields of the Hermitian function field. We compute the automorphism group, the Weierstrass semigroup at some special rational places and the isomorphism classes of such function fields. In this way, we show that often these function fields provide in fact examples of maximal function fields with the same genus, the same automorphism group, but that are not isomorphic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14179 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some families of non-isomorphic maximal function fields Beelen, Peter Montanucci, Maria Niemann, Jonathan Tilling Quoos, Luciane Number Theory Algebraic Geometry 11G, 14G The problem of understanding whether two given function fields are isomorphic is well-known to be difficult, particularly when the aim is to prove that an isomorphism does not exist. In this paper we investigate a family of maximal function fields that arise as Galois subfields of the Hermitian function field. We compute the automorphism group, the Weierstrass semigroup at some special rational places and the isomorphism classes of such function fields. In this way, we show that often these function fields provide in fact examples of maximal function fields with the same genus, the same automorphism group, but that are not isomorphic. |
| title | Some families of non-isomorphic maximal function fields |
| topic | Number Theory Algebraic Geometry 11G, 14G |
| url | https://arxiv.org/abs/2404.14179 |