论文标题
chabauty- chabauty方法和对数中的P-ADIC线性形式
The Chabauty--Coleman method and p-adic linear forms in logarithms
论文作者
论文摘要
结果$ p $ - 阿德超越理论适用于chabauty-coleman方法中的两个问题。首先是关于Coleman积分的重复根源的McCallum和Poonen的问题。第二个是根据雅各布式的一组Mordell-Weil发电机的高度，在理性点之间的$ p $ adadic距离上给出下限。我们还解释了在某些情况下，关于曲线雅各布人的“ Wieferich统计”的猜想是如何在曲线的通常不变的曲线及其雅各比亚人的mordell-weil生成器的高度方面绑定了小等级曲线的高度。该证明使用chabauty-coleman方法，以及超越理论中的有效方法。我们还讨论了chabauty-kim方法的概括。
Results in $p$-adic transcendence theory are applied to two problems in the Chabauty-Coleman method. The first is a question of McCallum and Poonen regarding repeated roots of Coleman integrals. The second is to give lower bounds on the $p$-adic distance between rational points in terms of the heights of a set of Mordell-Weil generators of the Jacobian. We also explain how, in some cases, a conjecture on the 'Wieferich statistics' of Jacobians of curves implies a bound on the height of rational points of curves of small rank, in terms of the usual invariants of the curve and the height of Mordell-Weil generators of its Jacobian. The proof uses the Chabauty-Coleman method, together with effective methods in transcendence theory. We also discuss generalisations to the Chabauty-Kim method.
