Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Courbes de genre 3 avec S3 comme groupe d'automorphismes   this paper is devoted to the study of curves of genus 3 with group of
automorphisms the symmetric group S3, principally over finite fields, in view
to obtain optimal curves. For instance, we prove that, over the finite fields
of char. 3, for any elliptic curve E with j-invariant not in F_3, there exists
a curve of genus 3 whose jacobian is isogeneous to E^3; we have also results in
char. 7, and these curves provide many examples of optimal curves in any char.
Nous etudions les courbes de genre 3 dont le groupe d'automorphismes est S3, en
vue d'obtenir des courbes optimales sur les corps finis. En particulier, en
car. 3, si E est unecourbe elliptique dont l'invariant n'est pas dans F_3, il
existe une telle courbe de genre 3 dont la jacobienne est isogene a E^3; dans
le cas de la caracteristique 7, des resultats plus partiels sont obtenus. Par
ailleurs, ces courbes semblent donner experimentalement de nombreux cas de
courbes optimales.

28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin