代数数论是现代数学研究中的一个重要分支，也是广大数学家广泛研究的重要领域. 近来, 被数学界统称的“Iwasawa主要猜想”逐渐成为数学家研究的焦点, 该猜想预测了塞尔默群和某些p进L函数的关系. 因此, 对塞尔默群构造的研究和了解将在一定程度上促进和加深对“Iwasawa主要猜想”的理解与应用, 同时也对“Iwasawa主要猜想”被具体化起着重要的作用. 近年来, 被数学家们热烈探讨的是p进表示的塞尔默群在一个无线数域塔的结构. 众所周知, 在经典情况下我们考虑的是当无线数域塔是Zp扩张的情形. 于是, 我们会自然而然地想到将此经典情况下的结论推广到一般的数域塔, 这其中最常被考虑到的是数域塔为p进李扩张的情况. 这个就是我现在的主要研究方向之一.

Algebraic number theory has been a fundamental and important research area in Mathematics. Recently, a widely studied subject in number theory is the so-called “Iwasawa main conjecture” . Such a conjecture gives an explicit relation between special values of p-adic L-functions and the algebraic structure of appropriate Selmer groups. An important step towards understanding this theory is to study the structure of the various Selmer groups which will in turn give great understanding towards the main conjecture. Currently, there has been many studies on understanding the structure of the Selmer groups of Galois representations defined over an p-adic Lie extension of a number field. The classical situation is concerned with the situation when the p-adic Lie extension is a Zp-extension. Our work is concerned with the general situation of a noncomutative p-adic Lie extension. This will be the main theme of our research project.