一、 課程背景與目的：

Class Field Theory is one of fundamental tools in number theory. Due to the growth of students who wish to explore the areas of number theory, arithmetic geometry and related topics, it is necessary to provide a course which cover Class Field Theory. In this short course we plan to cover Local Class Field Theory which partially meets the need. 

    

二、課程之大綱：

We will follow Serre’s Local Class Field Theory. The main topics are outline as follows:

1. The Brauer Group of a Local Field

2. Abelian extensions of Local Fields

3. Formal Multiplications in Local Fields

 

Reference:

Jean-Pierre Serre, Local Class Field Theory. Chapter in Algebraic Number Theory edited by Cassels and Frohlich, pp. 129--160