Geodesic
Zeta Functions of Bielliptic Surfaces over Finite Fields
Matematičeskie zametki, Tome 83 (2008) no. 2, pp. 273-285

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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, Albanese mapping, elliptic curve, étale cohomology, isogeny class.
Mots-clés : bielliptic surface, Frobenius morphism 
@article{MZM_2008_83_2_a8,
     author = {S. Yu. Rybakov},
     title = {Zeta {Functions} of {Bielliptic} {Surfaces} over {Finite} {Fields}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {273--285},
     publisher = {mathdoc},
     volume = {83},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_83_2_a8/}
}
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S. Yu. Rybakov. Zeta Functions of Bielliptic Surfaces over Finite Fields. Matematičeskie zametki, Tome 83 (2008) no. 2, pp. 273-285. http://geodesic.mathdoc.fr/item/MZM_2008_83_2_a8/