Governing fields for hyperelliptic function fields
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912395365974016 |
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| author | Stokvis, Joppe |
| author_facet | Stokvis, Joppe |
| contents | We study the 8-rank of class groups of hyperelliptic function fields and show that such 8-ranks are governed by splitting conditions in so-called governing fields. A similar result was proven for quadratic number fields by Stevenhagen, who used a theory of Rédei symbols and Rédei reciprocity to do so. We introduce a version of the Rédei reciprocity law for function fields and use this to show existence of governing fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20117 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Governing fields for hyperelliptic function fields Stokvis, Joppe Number Theory 11R11 (Primary), 11R58, 11R65 (Secondary) We study the 8-rank of class groups of hyperelliptic function fields and show that such 8-ranks are governed by splitting conditions in so-called governing fields. A similar result was proven for quadratic number fields by Stevenhagen, who used a theory of Rédei symbols and Rédei reciprocity to do so. We introduce a version of the Rédei reciprocity law for function fields and use this to show existence of governing fields. |
| title | Governing fields for hyperelliptic function fields |
| topic | Number Theory 11R11 (Primary), 11R58, 11R65 (Secondary) |
| url | https://arxiv.org/abs/2505.20117 |