Quadratic Chabauty: p-adic heights and integral points on hyperelliptic curves
Quadratic Chabauty: p-adic heights and integral points on hyperelliptic curves
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DOI：
10.1515/crelle-2014-0048
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发表时间：
2016-11-01
影响因子：
1.5
通讯作者：
Mueller, J. Steffen
中科院分区：
文献类型：
--
作者：
Balakrishnan, Jennifer S.;Besser, Amnon;Mueller, J. Steffen
给出了超椭圆曲线上0阶除数的p进高度对在p处的分量公式。当雅可比矩阵的Mordell-Weil秩等于格时，我们利用这一点给出了一种类似chabauty的方法来求此类曲线上p积分点的p进逼近。在这种情况下，我们得到了这种p积分点的数量的显式边界，并且我们能够在显式计算中使用该方法。该方法的一个重要方面是它只需要一个带有Q的莫德尔-韦尔群的基。
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.