Quadratic Chabauty and Rational Points II: Generalised Height Functions on Selmer Varieties

被引：9
作者：
Balakrishnan, Jennifer S. [1 ]
Dogra, Netan [2 ]
机构：
[1] Boston Univ, Dept Math & Stat, 111 Cummington Mall, Boston, MA 02215 USA
[2] Univ Oxford, Math Inst, Radcliffe Observ Quarter, Oxford OX2 6GG, England
来源：
INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2021年 / 2021卷 / 15期
基金：
英国工程与自然科学研究理事会;
关键词：
FUNDAMENTAL GROUP; COLEMAN INTEGRATION; GOOD REDUCTION; GALOIS ACTIONS; CURVES; GEOMETRY; THEOREM;
D O I：
10.1093/imrn/rnz362
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give new instances where Chabauty-Kim sets can be proved to be finite, by developing a notion of "generalised height functions" on Selmer varieties. We also explain how to compute these generalised heights in terms of iterated integrals and give the 1st explicit nonabelian Chabauty result for a curve X/Q whose Jacobian has Mordell-Weil rank larger than its genus.
引用
收藏
页码：11923 / 12008
页数：86
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