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Matematicheskie Zametki, 2016, Volume 99, Issue 3, Pages 384–394
DOI: https://doi.org/10.4213/mzm10747 (Mi mzm10747) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Classification of Zeta Functions of Bielliptic Surfaces over Finite Fields

S. Yu. Rybakovabc

a Institute for Information Transmission Problems, Russian Academy of Sciences
b Laboratoire J.-V. Poncelet, Independent University of Moscow
c Laboratory of algebraic geometry and its applications, Higher School of Economics, Moscow
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DOI: https://doi.org/10.4213/mzm10747
Abstract: Let $S$ be a bielliptic surface over a finite field, and let an elliptic curve $B$ be the Albanese variety of $S$; then the zeta function of the surface $S$ is equal to the zeta function of the direct product $\mathbb P^1\times B$. Therefore, the classification problem for the zeta functions of bielliptic surfaces is reduced to the existence problem for surfaces of a given type with a given Albanese curve. In the present paper, we complete this classification initiated in [1].
Keywords: finite field, zeta function, elliptic curve, bielliptic surface.
Funding agency Grant number
Russian Science Foundation 14-50-00150
The research was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences and was supported by the Russian Science Foundation under grant 14-50-00150.
Received: 05.03.2015
Revised: 12.07.2015
English version:
Mathematical Notes, 2016, Volume 99, Issue 3, Pages 397–405
DOI: https://doi.org/10.1134/S0001434616030081
Bibliographic databases:
Document Type: Article
MSC: 14G15 14G10
Language: Russian
Citation: S. Yu. Rybakov, “Classification of Zeta Functions of Bielliptic Surfaces over Finite Fields”, Mat. Zametki, 99:3 (2016), 384–394; Math. Notes, 99:3 (2016), 397–405
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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