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 50 条

[1] Groups of points on abelian threefolds over finite fields
Kotelnikova, Yulia
FINITE FIELDS AND THEIR APPLICATIONS, 2019, 58 : 177 - 199
[2] The groups of points on abelian varieties over finite fields
Rybakov, Sergey
CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2010, 8 (02): : 282 - 288
[3] Abelian surfaces over finite fields with prescribed groups
David, Chantal
Garton, Derek
Scherr, Zachary
Shankar, Arul
Smith, Ethan
Thompson, Lola
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2014, 46 : 779 - 792
[4] ABELIAN VARIETIES OVER FINITE FIELDS AND THEIR GROUPS OF RATIONAL POINTS
Marseglia, Stefano
Springer, Caleb
arXiv, 2022,
[5] Abelian varieties over finite fields and their groups of rational points
Marseglia, Stefano
Springer, Caleb
ALGEBRA & NUMBER THEORY, 2025, 19 (03)
[6] ON CLASSIFICATION OF GROUPS OF POINTS ON ABELIAN VARIETIES OVER FINITE FIELDS
Rybakov, Sergey
MOSCOW MATHEMATICAL JOURNAL, 2015, 15 (04) : 805 - 815
[7] On a classification of the automorphism groups of polarized abelian surfaces over finite fields
Hwang, WonTae
FINITE FIELDS AND THEIR APPLICATIONS, 2021, 72
[8] Abelian surfaces over finite fields as Jacobians
Maisner, D
Nart, E
Howe, EW
EXPERIMENTAL MATHEMATICS, 2002, 11 (03) : 321 - 337
[9] ON SUPERSPECIAL ABELIAN SURFACES OVER FINITE FIELDS
Xue, Jiangwei
Yang, Tse-Chung
Yu, Chia-Fu
DOCUMENTA MATHEMATICA, 2016, 21 : 1607 - 1643
[10] Distribution of points on Abelian covers over finite fields
Meisner, Patrick
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2018, 14 (05) : 1375 - 1401

← 1 2 3 4 5 →