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arXiv · 2507.10365

A ruled residue theorem for function fields of hyperelliptic curves

Parul Gupta·Sumit Chandra Mishra
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Abstract

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.

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Parul Gupta, Sumit Chandra Mishra. 2025-07-14. A ruled residue theorem for function fields of hyperelliptic curves. https://arxiv.org/abs/2507.10365

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