A ruled residue theorem for function fields of elliptic curves

Karim Johannes Becher; Parul Gupta; Sumit Chandra Mishra

doi:10.1016/j.jpaa.2023.107492

paper

A ruled residue theorem for function fields of elliptic curves

arXiv:2303.02100 · doi:10.1016/j.jpaa.2023.107492

Abstract

It is shown that a valuation of residue characteristic different from $2$ and $3$ on a field $E$ has at most one extension to the function field of an elliptic curve over $E$ , for which the residue field extension is transcendental but not ruled. The cases where such an extension is present are characterised.

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