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Mat. Zametki, 2016, Volume 99, Issue 3, Pages 384–394 (Mi mz10747)  

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

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.


DOI: https://doi.org/10.4213/mzm10747

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English version:
Mathematical Notes, 2016, 99:3, 397–405

Bibliographic databases:

Document Type: Article
MSC: 14G15 14G10
Received: 05.03.2015
Revised: 12.07.2015

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

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    This publication is cited in the following articles:
    1. S. G. Vlăduţ, D. Yu. Nogin, M. A. Tsfasman, “Varieties over finite fields: quantitative theory”, Russian Math. Surveys, 73:2 (2018), 261–322  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Математические заметки Mathematical Notes
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