ON THE NUMBER OF POINTS OF GIVEN ORDER ON ODD-DEGREE HYPERELLIPTIC CURVES

被引：1

作者：

Boxall, John ^{[1
]}

机构：

[1] Univ Caen Normandie, Lab Math Nicolas Oresme, UME CNRS 6139, F-14032 Caen, France

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2023年 / 53卷 / 02期

关键词：

hyperelliptic curves; Jacobian varieties; torsion points; TORSION POINTS; DIVISION;

D O I：

10.1216/rmj.2023.53.357

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For integers N & GE; 2 and g & GE; 1, we study bounds on the cardinality of the set of points of order dividing N lying on a hyperelliptic curve of genus g embedded in its jacobian using a Weierstrass point as base point. This leads us to revisit division polynomials introduced by Cantor in 1995 and strengthen a divisibility result proved by him. Several examples are discussed.

引用

页码：357 / 382

页数：26

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