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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 22 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}
}

Comments

14 pages

R2 v1 2026-06-23T11:31:47.274Z