Geodesic
Classification of Zeta Functions of Bielliptic Surfaces over Finite Fields
Matematičeskie zametki, Tome 99 (2016) no. 3, pp. 384-394

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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 $\mathbb P^1\times B$. 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].
Keywords: finite field, zeta function, elliptic curve
Mots-clés : bielliptic surface. 
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     author = {S. Yu. Rybakov},
     title = {Classification of {Zeta} {Functions} of {Bielliptic} {Surfaces} over {Finite} {Fields}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {384--394},
     publisher = {mathdoc},
     volume = {99},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_3_a7/}
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S. Yu. Rybakov. Classification of Zeta Functions of Bielliptic Surfaces over Finite Fields. Matematičeskie zametki, Tome 99 (2016) no. 3, pp. 384-394. http://geodesic.mathdoc.fr/item/MZM_2016_99_3_a7/