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

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arXiv · 2303.02100

A ruled residue theorem for function fields of elliptic curves

Karim Johannes Becher·Parul Gupta·Sumit Chandra Mishra

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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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Karim Johannes Becher, Parul Gupta, Sumit Chandra Mishra. 2023-06-29. A ruled residue theorem for function fields of elliptic curves. https://doi.org/10.1016/j.jpaa.2023.107492

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