代数K-理论与代数数论相互渗透的一些问题是目前学界的前沿热门课题之一。本项目主要针对代数数域整数环的K2群展开研究工作。项目的研究内容分为：1）代数整数环上的K2群的代数结构的研究，深入讨论Abel数域及非Abel数域的代数整数环K2群的p-rank公式，讨论数域tame核与其子域tame核之间的关系，研究数域tame核与其类群之间的联系，得到有关类数的新结果；2）代数整数环的K2群的密度分布问题，发现一些特殊数域的代数整数环的K2群的密度分布的结果，将函数域上的相关密度研究成果，推广至代数数域情况。项目申请人理论基础扎实，且在前期研究中已经取得了部分成果。

The problems between the algebraic K-theory and the algebraic number theory are one of the hot topics in academia. This project will study the questions about the K2 groups of the rings of integers in the algebraic number fields. We will study the following topics: 1) Research on structure of the K2 groups of the rings of integers. We will study the p-rank of K2 groups of the rings of integers. We will discuss the relations between the tame kernels of algebraic number fields and ideal class groups; 2) The problems on the density of the K2 group of the rings of integers. We will study the densities of the K2 groups of the rings of integers about some algebraic number fields. We will generalize the Cohen-Lenstra conjecture in function fields to algebraic K-group. The applicants have rich research experience in this area, and have obtained some results.