The groups of points on abelian varieties over finite fields

被引：12

作者：

Rybakov, Sergey ^{[1
,2
,3
]}

机构：

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

[2] Independent Univ Moscow, Moscow, Russia

[3] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow 117901, Russia

来源：

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS | 2010年 / 8卷 / 02期

关键词：

Abelian variety; The group of rational points; Finite field; Newton polygon; Hodge polygon; ELLIPTIC-CURVES;

D O I：

10.2478/s11533-010-0003-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A be an abelian variety with commutative endomorphism algebra over a finite field k. The k-isogeny class of A is uniquely determined by a Weil polynomial f (A) without multiple roots. We give a classification of the groups of k-rational points on varieties from this class in terms of Newton polygons of f (A) (1 - t).

引用

页码：282 / 288

页数：7

共 12 条

[1]

[Anonymous], ANN SCI ECOLE NORM S

[2]

[Anonymous], 1985, THEORY NUMBERS ITS A

[3]

Berthelot Pierre, 1978, Notes on Crystalline Cohomology

[4]

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

[5]

KEDLAYA K, P ADIC DIFF IN PRESS

[6] A NOTE ON ELLIPTIC-CURVES OVER FINITE-FIELDS [J].

RUCK, HG .

MATHEMATICS OF COMPUTATION, 1987, 49 (179) :301-304

[7] NONSINGULAR PLANE CUBIC CURVES OVER FINITE-FIELDS [J].

SCHOOF, R .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 1987, 46 (02) :183-211

[8]

Tsfasman Michael, 2007, Algebraic Geometric Codes: Basic Notions

[9] A NOTE ON ELLIPTIC-CURVES OVER FINITE-FIELDS [J].

VOLOCH, JF .

BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 1988, 116 (04) :455-458

[10]

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

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