The groups of points on abelian surfaces over finite fields

被引：6

作者：

Rybakov, Sergey ^{[1
]}

机构：

[1] CNRS, UMI 2615, Poncelet Lab, F-75700 Paris, France

来源：

ARITHMETIC, GEOMETRY, CRYPTOGRAPHY AND CODING THEORY | 2012年 / 574卷

关键词：

Abelian variety; the group of rational points; finite field; Newton polygon; Hodge polygon; VARIETIES;

D O I：

10.1090/conm/574/11424

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A be an abelian surface over a finite field k. The k-isogeny class of A is uniquely determined by a Weil polynomial f(A) of degree 4. We give a classification of the groups of k-rational points on varieties from this class in terms of f(A).

引用

页码：151 / 158

页数：8

共 10 条

[1]

Berthelot Pierre, 1978, Notes on Crystalline Cohomology

[2]

DEMAZURE M., 1972, Lecture Notes in Mathematics, V302

[3]

Kedlaya K., 2010, RHO ACID DIFFERENTIA

[4] Abelian surfaces over finite fields as Jacobians [J].

Maisner, D ;

Nart, E ;

Howe, EW .

EXPERIMENTAL MATHEMATICS, 2002, 11 (03) :321-337

[5]

Rybakov S., ARXIV10065959V1

[6] The groups of points on abelian varieties over finite fields [J].

Rybakov, Sergey .

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2010, 8 (02) :282-288

[7]

Waterhouse W.C., 1969, P S PURE MATH, VXX, P53

[8]

Waterhouse WC., 1969, ANN SCI ECOLE NORM S, V2, P521, DOI 10.24033/asens.1183

[9]

Xing C., 1996, Finite Fields Appl, V2, P407, DOI [DOI 10.1006/FFTA.1996.0024, 10.1006/ffta.1996.0024]

[10] THE STRUCTURE OF THE RATIONAL POINT GROUPS OF SIMPLE ABELIAN-VARIETIES OF DIMENSION 2 OVER FINITE-FIELDS [J].

XING, CP .

ARCHIV DER MATHEMATIK, 1994, 63 (05) :427-430

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