Introduction to Galois Cohomology and Local Class Field Theory

任课教师 Speaker:任金波(弗吉尼亚大学)
时间 Time: 每周一、三13:30-15:05, 2019-6-3 ~7-3(6月10、12日17:05-18:40)
地点 Venue:清华大学近春园西楼第一会议室(6月10日近春园西楼第三会议室)

课程描述 Description

This short course consists of two main subjects: Galois Cohomology and Class field theory.
Understanding the Galois group of a local field or a number field is one of the fundamental objectives in number theory. Galois Cohomology is the application of homological algebra to the structure of Galois groups.
Concerning Class field theory, it is, roughly speaking, the 1-dimensional case of the Langlands Program.
In this short course, I am going to introduce the basic theory of Galois Cohomology together with its applications in Class field theory.

预备知识 Prerequisites

Abstract algebra (including Galois theory and module theory).
In our course we also need some notions and results in algebraic number theory (including local fields). Knowledge of these is convenient, but not necessary, since we will recall what is needed during the course.

参考资料 References

[1] J. Neukirch. Algebraic number theory, volume 322 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, 1999.
[2] J.-P. Serre, Local fields, Graduate Texts in Mathematics 67, Springer-Verlag, New York–Berlin, 1979.
[3] J.-P. Serre, Galois Cohomology, Springer Monographs in Mathematics, Springer Verlag, Berlin, 2002.
Further references will be mentioned during lectures.