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Mat. Zametki, 2008, Volume 83, Issue 2, Pages 273–285 (Mi mz4419)  

This article is cited in 2 scientific papers (total in 2 papers)

Zeta Functions of Bielliptic Surfaces over Finite Fields

S. Yu. Rybakov

Independent University of Moscow

Abstract: Let $S$ be a bielliptic surface over a finite field, and let the elliptic curve $B$ be the image of the Albanese mapping $S\to B$. In this case, the zeta function of the surface is equal to the zeta function of the direct product $\mathbb P^1\times B$. A classification of the possible zeta functions of bielliptic surfaces is also presented in the paper.

Keywords: variety over a finite field, zeta function, bielliptic surface, Albanese mapping, elliptic curve, étale cohomology, Frobenius morphism, isogeny class

DOI: https://doi.org/10.4213/mzm4419

Full text: PDF file (521 kB)
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English version:
Mathematical Notes, 2008, 83:2, 246–256

Bibliographic databases:

UDC: 512.754
Received: 03.04.2007

Citation: S. Yu. Rybakov, “Zeta Functions of Bielliptic Surfaces over Finite Fields”, Mat. Zametki, 83:2 (2008), 273–285; Math. Notes, 83:2 (2008), 246–256

Citation in format AMSBIB
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\paper Zeta Functions of Bielliptic Surfaces over Finite Fields
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\pages 273--285
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\pages 246--256
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  • https://doi.org/10.4213/mzm4419
  • http://mi.mathnet.ru/eng/mz/v83/i2/p273

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. Yu. Rybakov, “Classification of Zeta Functions of Bielliptic Surfaces over Finite Fields”, Math. Notes, 99:3 (2016), 397–405  mathnet  crossref  crossref  mathscinet  isi  elib
    2. 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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