On the asymptotics of elementary-abelian extensions of local and global function fields
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916779714936832 |
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| author | Potthast, Nicolas |
| author_facet | Potthast, Nicolas |
| contents | We determine the distribution of discriminants of wildly ramified elementary-abelian extensions of local and global function fields in characteristic $p$. For local and rational function fields, we also give precise formulae for the number of elementary-abelian extensions with a fixed discriminant divisor, which describe a local-global principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16394 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the asymptotics of elementary-abelian extensions of local and global function fields Potthast, Nicolas Number Theory 11R45 (Primary) 11R37, 11S31 (Secondary) We determine the distribution of discriminants of wildly ramified elementary-abelian extensions of local and global function fields in characteristic $p$. For local and rational function fields, we also give precise formulae for the number of elementary-abelian extensions with a fixed discriminant divisor, which describe a local-global principle. |
| title | On the asymptotics of elementary-abelian extensions of local and global function fields |
| topic | Number Theory 11R45 (Primary) 11R37, 11S31 (Secondary) |
| url | https://arxiv.org/abs/2408.16394 |