Classification of zeta functions of bielliptic surfaces over finite fields

被引：1

作者：

Rybakov, S. Yu. ^{[1
,2
,3
]}

机构：

[1] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow, Russia

[2] Independent Univ Moscow, Lab Poncelet, Moscow, Russia

[3] Natl Res Univ, Higher Sch Econ, Lab Algebra Geometry & Its Applicat, Moscow, Russia

来源：

MATHEMATICAL NOTES | 2016年 / 99卷 / 3-4期

基金：

俄罗斯科学基金会;

关键词：

finite field; zeta function; elliptic curve; bielliptic surface;

D O I：

10.1134/S0001434616030081

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 P-1 x 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].

引用

页码：397 / 405

页数：9

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