A ruled residue theorem for function fields of hyperelliptic curves
Commutative Algebra
2025-07-15 v1
Abstract
We study residually transcendental extensions of a valuation on a field to function fields of hyperelliptic curves over . We show that has at most finitely many extensions to the function field of a hyperelliptic curve over , for which the residue field extension is transcendental but not ruled, assuming that the residue characteristic of is either zero or greater than the degree of the hyperelliptic curve.
Keywords
Cite
@article{arxiv.2507.10365,
title = {A ruled residue theorem for function fields of hyperelliptic curves},
author = {Parul Gupta and Sumit Chandra Mishra},
journal= {arXiv preprint arXiv:2507.10365},
year = {2025}
}