A ruled residue theorem for function fields of conics
Commutative Algebra
2020-11-12 v3 Algebraic Geometry
Abstract
The ruled residue theorem characterises residue field extensions for valuations on a rational function field. Under the assumption that the characteristic of the residue field is different from this theorem is extended here to function fields of conics. The main result is that there is at most one extension of a valuation from on the base field to the function field of a conic for which the residue field extension is transcendental but not ruled. Furthermore the situation when this valuation is present is characterised.
Keywords
Cite
@article{arxiv.1910.00479,
title = {A ruled residue theorem for function fields of conics},
author = {Parul Gupta and Karim Johannes Becher},
journal= {arXiv preprint arXiv:1910.00479},
year = {2020}
}
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14 pages