Classification of zeta functions of bielliptic surfaces over finite fields
- 24 Downloads
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 .
Keywordsfinite field zeta function elliptic curve bielliptic surface
Unable to display preview. Download preview PDF.
- 2.M. A. Tsfasman, “Nombre de points des surfaces sur un corps fini,” in Arithmetic, Geometry and Coding Theory (Walter de Gruyter, Berlin, 1996), pp. 209–224.Google Scholar
- 6.M. Demazure, Lectures on p-Divisible Groups, in Lecture Notes in Math. (Springer-Verlag, Berlin, 1972), Vol. 302.Google Scholar
- 9.M. A. Tsfasman, “Group of points of an elliptic curve over a finite field,” in Theory of Numbers and Its Applications (Tbilisi, 1985), pp. 286–287.Google Scholar
- 11.L. Badescu, Algebraic Surfaces, in Universitext (Springer-Verlag, New York, 2001).Google Scholar