ON CLASSIFICATION OF GROUPS OF POINTS ON ABELIAN VARIETIES OVER FINITE FIELDS

被引:2
|
作者
Rybakov, Sergey [1 ,2 ]
机构
[1] Russian Acad Sci, Inst Informat Transmiss Problems, Poncelet Lab, UMI 2615,CNRS, 7 Vavilova Str, Moscow 117312, Russia
[2] Independent Univ Moscow, AG Lab, HSE, Moscow 117312, Russia
关键词
Aelian variety; the group of rational points; finite field; Newton polygon; Hodge polygon;
D O I
10.17323/1609-4514-2015-15-4-805-815
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper we improve our previous results on classification of groups of points on abelian varieties over finite fields. The classification is given in terms of the Weil polynomial of abelian varieties in a given kappa-is ogeny class over a finite field kappa.
引用
收藏
页码:805 / 815
页数:11
相关论文
共 50 条
  • [1] The groups of points on abelian varieties over finite fields
    Rybakov, Sergey
    [J]. CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2010, 8 (02): : 282 - 288
  • [2] ABELIAN VARIETIES OVER FINITE FIELDS AND THEIR GROUPS OF RATIONAL POINTS
    Marseglia, Stefano
    Springer, Caleb
    [J]. arXiv, 2022,
  • [3] Groups of points on abelian threefolds over finite fields
    Kotelnikova, Yulia
    [J]. FINITE FIELDS AND THEIR APPLICATIONS, 2019, 58 : 177 - 199
  • [4] The groups of points on abelian surfaces over finite fields
    Rybakov, Sergey
    [J]. ARITHMETIC, GEOMETRY, CRYPTOGRAPHY AND CODING THEORY, 2012, 574 : 151 - 158
  • [5] On the number of points on abelian and Jacobian varieties over finite fields
    Aubry, Yves
    Haloui, Safia
    Lachaud, Gilles
    [J]. ACTA ARITHMETICA, 2013, 160 (03) : 201 - 241
  • [6] Counting points on curves and Abelian varieties over finite fields
    Adleman, LM
    Huang, MD
    [J]. JOURNAL OF SYMBOLIC COMPUTATION, 2001, 32 (03) : 171 - 189
  • [7] On the number of points on abelian and Jacobian varieties over finite fields
    Aubry, Yves
    Haloui, Safia
    Lachaud, Gilles
    [J]. COMPTES RENDUS MATHEMATIQUE, 2012, 350 (19-20) : 907 - 910
  • [8] On the cyclicity of the rational points group of abelian varieties over finite fields
    Giangreco-Maidana, Alejandro J.
    [J]. FINITE FIELDS AND THEIR APPLICATIONS, 2019, 57 : 139 - 155
  • [9] Counting rational points on curves and abelian varieties over finite fields
    Adleman, LM
    Huang, MDA
    [J]. ALGORITHMIC NUMBER THEORY, 1996, 1122 : 1 - 16
  • [10] Abelian varieties over finite fields as basic abelian varieties
    Yu, Chia-Fu
    [J]. FORUM MATHEMATICUM, 2017, 29 (02) : 489 - 500