Research on heights on algebraic varietiesfrom the viewpoint of Arakelov geometry and its application

在代数变量上，即由代数方程定义的几何对象，我们有时有“高度函数”。这些高度函数衡量了变种的算术复杂度。利用它们，我们可以研究小代数点的分布与品种的几何性质之间的关系。在本研究中，我们探讨了代数几何中一些重要学科的高度。此外，我们将关于高度的结果应用于有趣的算术问题，得到了显著的结果。

On an algebraic variety, which is a geometric object defined by algebraic equations, we sometimes have “height functions”. These height functions measure arithmetic complexity of varieties. Using them, we can study relationships between the distribution of small algebraic points and the geometric property of the variety. In this research, we investigated the heights of some important subjects in algebraic geometry. Furthermore, we applied the results on heights to interesting arithmetic problems, obtaining significant results.