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.
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