模态方案上的积分点

Pub Date : 2024-08-30 DOI:10.1016/j.jnt.2024.07.005

Rafael von Känel

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引用次数: 0

摘要

将法尔廷斯方法（Arakelov, Paršin, Szpiro）与模块性和马塞尔-伍斯特霍尔茨同源估计相结合的策略，可以明确约束与无常变体模态上积分点有关的某些二叉方程的解的高度和数目。在本文中，我们将考察这一策略的发展和各种应用。

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Integral points on moduli schemes

The strategy of combining the method of Faltings (Arakelov, Paršin, Szpiro) with modularity and Masser–Wüstholz isogeny estimates allows to explicitly bound the height and the number of the solutions of certain Diophantine equations related to integral points on moduli schemes of abelian varieties. In this paper we survey the development and various applications of this strategy.

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