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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/2404.17566 |
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| _version_ | 1866914772089307136 |
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| author | Hernandez-Bocanegra, Juan Carlos Villa-Salvador, Gabriel |
| author_facet | Hernandez-Bocanegra, Juan Carlos Villa-Salvador, Gabriel |
| contents | In this paper we obtain the extended genus field of a finite abelian extension of a global rational function field. We first study the case of a cyclic extension of prime power degree. Next, we use that the extended genus fields of a composite of two cyclotomic extensions of a global rational function field is equal to the composite of their respective extended genus fields, to obtain our main result. This result is that the extended genus field of a general finite abelian extension of a global rational function field, is given explicitly in terms of the field and of the extended genus field of its "cyclotomic projection". |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17566 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extended genus fields of abelian extensions of rational function fields Hernandez-Bocanegra, Juan Carlos Villa-Salvador, Gabriel Number Theory In this paper we obtain the extended genus field of a finite abelian extension of a global rational function field. We first study the case of a cyclic extension of prime power degree. Next, we use that the extended genus fields of a composite of two cyclotomic extensions of a global rational function field is equal to the composite of their respective extended genus fields, to obtain our main result. This result is that the extended genus field of a general finite abelian extension of a global rational function field, is given explicitly in terms of the field and of the extended genus field of its "cyclotomic projection". |
| title | Extended genus fields of abelian extensions of rational function fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2404.17566 |