代数整数环上K-群及相关问题的研究

代数K-理论中著名的Lichtenbaum猜想建立了代数K-理论与代数数论之间的深刻联系, 使得它们之间的一些问题互相渗透, 相互促进发展, 其中代数整数环上K-群及其相关问题的研究是代数K-理论领域中的前沿课题. 本项目将围绕Lichtenbaum猜想开展研究, 主要研究内容为: 代数整数环上的高阶类数、Tame核结构、代数K-理论在代数数论中的应用以及与子集和相关问题的研究. 项目组成员将在已有的研究基础上, 拓展研究思路, 发展新的研究方法, 获得预期的新成果, 解决一些重要问题, 例如与Birch-Tate猜想和Lichtenbaum猜想有关的问题.

The Lichtenbaum conjecture in the field of algebraic K- theory established the deep connection between algebraic K- theory and algebraic number theory, which makes some problems among them permeate and promotes each other's development. Among them, research on K-groups of the ring of algebraic integers and related problems is the advanced subject in the field of algebraic K- theory. This project will focus on the Lichtenbaum conjecture, mainly including: higher class numbers of the ring of algebraic integers, the structure of Tame kernels, the applications of algebraic K- theory to algebraic number theory and some problems related to subset sums. Based on the existing research, we will expand research ideas, develop new research methods, make significant progress, and solve some important problems, such as those related to the Birch-Tate conjecture and the Lichtenbaum conjecture.