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This article is cited in 7 scientific papers (total in 7 papers)
Minimal cubic surfaces over finite fields
S. Yu. Rybakov, A. S. Trepalin Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
Abstract:
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, del Pezzo surface.
Received: 12.12.2016 and 05.04.2017
Citation:
S. Yu. Rybakov, A. S. Trepalin, “Minimal cubic surfaces over finite fields”, Sb. Math., 208:9 (2017), 1399–1419
Linking options:
https://www.mathnet.ru/eng/sm8880https://doi.org/10.1070/SM8880 https://www.mathnet.ru/eng/sm/v208/i9/p148
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Abstract page: | 443 | Russian version PDF: | 84 | English version PDF: | 18 | References: | 43 | First page: | 21 |
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