Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A ruled residue theorem for function fields of conics   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 $2$ 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.

6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th