Quadratic Chabauty and Rational Points II: Generalised Height Functions on Selmer Varieties
Quadratic Chabauty and Rational Points II: Generalised Height Functions on Selmer Varieties
复制标题
DOI：
10.1093/imrn/rnz362
复制
发表时间：
2017-05
影响因子：
1
通讯作者：
Jennifer S. Balakrishnan;Netan Dogra
中科院分区：
文献类型：
--
作者：
Jennifer S. Balakrishnan;Netan Dogra
我们给出了新的例子，Chabauty-金集可以被证明是有限的，通过发展的概念“广义高度函数”的塞尔默品种。我们还解释了如何计算这些广义高度的迭代积分，并给出了第一显式nonabelian Chabauty结果的曲线$X/\mathbb{Q}$的雅可比矩阵的Mordell-Weil秩大于其属。
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 $X/\mathbb{Q}$ whose Jacobian has Mordell–Weil rank larger than its genus.