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Sbornik: Mathematics, 2017, Volume 208, Issue 9, Pages 1399–1419
DOI: https://doi.org/10.1070/SM8880
(Mi sm8880)
 

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
References:
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.
Funding agency Grant number
Russian Science Foundation 14-50-00150
This research was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences with the financial support of the Russian Science Foundation (project no. 14-50-00150).
Received: 12.12.2016 and 05.04.2017
Bibliographic databases:
Document Type: Article
UDC: 512.774.7
MSC: Primary 11G25; Secondary 14J20
Language: English
Original paper language: Russian
Citation: S. Yu. Rybakov, A. S. Trepalin, “Minimal cubic surfaces over finite fields”, Sb. Math., 208:9 (2017), 1399–1419
Citation in format AMSBIB
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\by S.~Yu.~Rybakov, A.~S.~Trepalin
\paper Minimal cubic surfaces over finite fields
\jour Sb. Math.
\yr 2017
\vol 208
\issue 9
\pages 1399--1419
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Linking options:
  • https://www.mathnet.ru/eng/sm8880
  • https://doi.org/10.1070/SM8880
  • https://www.mathnet.ru/eng/sm/v208/i9/p148
  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник Sbornik: Mathematics
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    Abstract page:443
    Russian version PDF:84
    English version PDF:18
    References:43
    First page:21
     
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