A flexible method for applying Chabauty's Theorem

被引：46

作者：

Flynn, EV

机构：

[1] Department of Pure Mathematics, University of Liverpool, Liverpool, L69 3BX

来源：

COMPOSITIO MATHEMATICA | 1997年 / 105卷 / 01期

关键词：

Jacobians; curves; rational points; Chabauty; formal groups;

D O I：

10.1023/A:1000111601294

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A strategy is proposed for applying Chabauty's Theorem to hyperelliptic curves of genus > 1. In the genus 2 case, it shown how recent developments on the formal group of the Jacobian can be used to give a flexible and computationally viable method for applying this strategy. The details are described for a general curve of genus 2, and are then applied to find C(Q) for a selection of curves. A fringe benefit is a more explicit proof of a result of Coleman.

引用

页码：79 / 94

页数：16

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[3]

CASSELS JWS, 1983, ARITHMETIC GEOMETRY, V1, P29

[4]

Chabauty C, 1941, CR HEBD ACAD SCI, V212, P882