Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On rationality of the intersection points of a line with a plane quartic   We study the rationality of the intersection points of certain lines and
smooth plane quartics C defined over F_q. For q \geq 127, we prove the
existence of a line such that the intersection points with C are all rational.
Using another approach, we further prove the existence of a tangent line with
the same property as soon as the characteristic of F_q is different from 2 and
q \geq 66^2+1. Finally, we study the probability of the existence of a rational
flex on C and exhibit a curious behavior when the characteristic of F_q is
equal to 3.

21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
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The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin