Quadratic Chabauty: p-adic heights and integral points on hyperelliptic curves

被引：23

作者：

Balakrishnan, Jennifer S. ^{[1
]}

Besser, Amnon ^{[2
]}

Mueller, J. Steffen ^{[3
]}

机构：

[1] Univ Oxford, Math Inst, Radcliffe Observ Quarter, Andrew Wiles Bldg,Woodstock Rd, Oxford OX2 6GG, England

[2] Ben Gurion Univ Negev, Dept Math, POB 653, IL-84105 Beer Sheva, Israel

[3] Univ Hamburg, Fachbereich Math, Bundesstr 55, D-20146 Hamburg, Germany

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2016年 / 720卷

基金：

英国工程与自然科学研究理事会;

关键词：

SELMER VARIETIES; FUNDAMENTAL GROUP; ELLIPTIC-CURVES;

D O I：

10.1515/crelle-2014-0048

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a formula for the component at p of the p-adic height pairing of a divisor of degree 0 on a hyperelliptic curve. We use this to give a Chabauty-like method for finding p-adic approximations to p-integral points on such curves when the Mordell-Weil rank of the Jacobian equals the genus. In this case we get an explicit bound for the number of such p-integral points, and we are able to use the method in explicit computation. An important aspect of the method is that it only requires a basis of the Mordell-Weil group tensored with Q.

引用

页码：51 / 79

页数：29

共 43 条

[31] MASSEY PRODUCTS FOR ELLIPTIC CURVES OF RANK 1 [J].