Mathematical Notes

, Volume 99, Issue 3–4, pp 397–405 | Cite as

Classification of zeta functions of bielliptic surfaces over finite fields

  • S. Yu. Rybakov


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 P1 × 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].


finite field zeta function elliptic curve bielliptic surface 


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© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Institute for Information Transmission ProblemsRussian Academy of SciencesMoscowRussia
  2. 2.Laboratoire PonceletIndependent University of MoscowMoscowRussia
  3. 3.Laboratory of Algebraic Geometry and Its ApplicationsNational Research University Higher School of EconomicsMoscowRussia

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