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Mosc. Math. J., 2005, Volume 5, Number 4, Pages 919–926 (Mi mmj228)  

This article is cited in 7 scientific papers (total in 7 papers)

Zeta functions of conic bundles and Del Pezzo surfaces of degree 4 over finite fields

S. Yu. Rybakov

Independent University of Moscow

Abstract: First of all, we construct a conic bundle with a prescribed zeta function. This is a key step to classify Del Pezzo surfaces of degree 4 over a finite field. In particular, we see that the zeta function determines the combinatorics of a Del Pezzo surface.

Key words and phrases: Zeta function, conic bundle, surface over a finite field, Del Pezzo surface.

Full text: http://www.ams.org/.../abst5-4-2005.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 11R58, 14G15, 11M38, 14G05
Received: October 1, 2005
Language: English

Citation: S. Yu. Rybakov, “Zeta functions of conic bundles and Del Pezzo surfaces of degree 4 over finite fields”, Mosc. Math. J., 5:4 (2005), 919–926

Citation in format AMSBIB
\Bibitem{Ryb05}
\by S.~Yu.~Rybakov
\paper Zeta functions of conic bundles and Del Pezzo surfaces of degree~4 over finite fields
\jour Mosc. Math.~J.
\yr 2005
\vol 5
\issue 4
\pages 919--926
\mathnet{http://mi.mathnet.ru/mmj228}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2266465}
\zmath{https://zbmath.org/?q=an:1130.14021}


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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, “Zeta Functions of Bielliptic Surfaces over Finite Fields”, Math. Notes, 83:2 (2008), 246–256  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Harada Sh., “Hasse-Weil Zeta Functions of Sl2-Character Varieties of Arithmetic Two-Bridge Link Complements”, Finite Fields their Appl., 27 (2014), 115–129  crossref  mathscinet  zmath  isi  scopus
    3. Knecht A., “Degree of Unirationality For Del Pezzo Surfaces Over Finite Fields”, J. Theor. Nr. Bordx., 27:1 (2015), 171–182  crossref  mathscinet  zmath  isi
    4. 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
    5. S. Yu. Rybakov, A. S. Trepalin, “Minimal cubic surfaces over finite fields”, Sb. Math., 208:9 (2017), 1399–1419  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. Trepalin A., “Minimal Del Pezzo Surfaces of Degree 2 Over Finite Fields”, Bull. Korean. Math. Soc., 54:5 (2017), 1779–1801  crossref  zmath  isi  scopus
    7. 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
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