Geodesic
Minimal cubic surfaces over finite fields
Sbornik. Mathematics, Tome 208 (2017) no. 9, pp. 1399-1419

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $X$ be a minimal cubic surface over a finite field $\mathbb{F}_q$. The image $\Gamma$ of the Galois group $\operatorname{Gal}(\overline{\mathbb{F}}_q / \mathbb{F}_q)$ in the group $\operatorname{Aut}(\operatorname{Pic}(\overline{X}))$ is a cyclic subgroup of the Weyl group $W(E_6)$. There are $25$ conjugacy classes of cyclic subgroups in $W(E_6)$, and five of them correspond to minimal cubic surfaces. It is natural to ask which conjugacy classes come from minimal cubic surfaces over a given finite field. In this paper we give a partial answer to this question and present many explicit examples. Bibliography: 11 titles.
Keywords: finite field, cubic surface, zeta function
Mots-clés : del Pezzo surface. 
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     author = {S. Yu. Rybakov and A. S. Trepalin},
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S. Yu. Rybakov; A. S. Trepalin. Minimal cubic surfaces over finite fields. Sbornik. Mathematics, Tome 208 (2017) no. 9, pp. 1399-1419. http://geodesic.mathdoc.fr/item/SM_2017_208_9_a6/