代数K-理论与算术动力系统相关问题的研究

本项目将致力于代数 K-理论和算术动力系统中下列相关问题的研究并取得新的成果：动态模曲线的 K-理论和 Mahler测度之间的关系、上同调和 K-理论中动力系统的算术及其应用、Northcott 有限性、动力系统中一致有界猜想以及Iwasawa理论、椭圆曲线的算术理论及其应用. 研究中使用并且发展我们已有的独创方法.

This project seeks to make significant progress in the study of the following related problems: the relationship between the K-theory of dynatomic modular curves and the Mahler measure, the arithmetic of dynamical systems in cohomology and K-theory and its application, Northcott finiteness、uniformly bounded conjecture and Iwasawa theory in arithmetical dynamical systems、the arithmetic of elliptic curve and its application. We will develop useful techniques to strengthen our original methods.