Kummer theory for function fields
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909255503708160 |
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| author | Boudreau, Félix Baril Perucca, Antonella |
| author_facet | Boudreau, Félix Baril Perucca, Antonella |
| contents | We develop Kummer theory for algebraic function fields in finitely many transcendental variables. We consider any finitely generated Kummer extension (possibly, over a cyclotomic extension) of an algebraic function field, and describe the structure of its Galois group. Our results show in a precise sense how the questions of computing the degrees of these extensions and of computing the group structures of their Galois groups reduce to the corresponding questions for the Kummer extensions of their constant fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10783 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kummer theory for function fields Boudreau, Félix Baril Perucca, Antonella Number Theory 11R18, 11R32, 11R58, 11R60, 11T22 We develop Kummer theory for algebraic function fields in finitely many transcendental variables. We consider any finitely generated Kummer extension (possibly, over a cyclotomic extension) of an algebraic function field, and describe the structure of its Galois group. Our results show in a precise sense how the questions of computing the degrees of these extensions and of computing the group structures of their Galois groups reduce to the corresponding questions for the Kummer extensions of their constant fields. |
| title | Kummer theory for function fields |
| topic | Number Theory 11R18, 11R32, 11R58, 11R60, 11T22 |
| url | https://arxiv.org/abs/2407.10783 |