A ruled residue theorem for function fields of hyperelliptic curves
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916843056267264 |
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| author | Gupta, Parul Mishra, Sumit Chandra |
| author_facet | Gupta, Parul Mishra, Sumit Chandra |
| contents | We study residually transcendental extensions of a valuation $v$ on a field $E$ to function fields of hyperelliptic curves over $E$. We show that $v$ has at most finitely many extensions to the function field of a hyperelliptic curve over $E$, for which the residue field extension is transcendental but not ruled, assuming that the residue characteristic of $v$ is either zero or greater than the degree of the hyperelliptic curve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10365 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A ruled residue theorem for function fields of hyperelliptic curves Gupta, Parul Mishra, Sumit Chandra Commutative Algebra 12F20, 12J10, 12J20, 14H05, 16H05 We study residually transcendental extensions of a valuation $v$ on a field $E$ to function fields of hyperelliptic curves over $E$. We show that $v$ has at most finitely many extensions to the function field of a hyperelliptic curve over $E$, for which the residue field extension is transcendental but not ruled, assuming that the residue characteristic of $v$ is either zero or greater than the degree of the hyperelliptic curve. |
| title | A ruled residue theorem for function fields of hyperelliptic curves |
| topic | Commutative Algebra 12F20, 12J10, 12J20, 14H05, 16H05 |
| url | https://arxiv.org/abs/2507.10365 |