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
收藏
页码:51 / 79
页数:29
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