Zeta functions of bielliptic surfaces over finite fields

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 → B. In this case, the zeta function of the surface is equal to the zeta function of the direct product ℙ1 × B. A classification of the possible zeta functions of bielliptic surfaces is also presented in the paper.