Class field theory
The goal of class field theory is to describe the Galois extensions of a local or global field in terms of the arithmetic of the field itself. For abelian extensions, the theory was developed between roughly 1850 and 1930 by Kronecker, Weber, Hilbert, Takagi, Artin, Hasse, and others. This course begins with an analysis of the quadratic case of Class Field Theory via Hilbert symbols, in order to give a more hands-on introduction to the ideas of Class Field Theory. More advanced topics in number theory are discussed in this course, such as Galois cohomology, proofs of class field theory, modular forms and automorphic forms, Galois representations, and quadratic forms.
Lecturer
Chuangqiang Hu
Date
18th September ~ 18th December, 2023
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Monday,Wednesday | 09:50 - 11:25 | A3-2-201 | ZOOM 08 | 787 662 9899 | BIMSA |
Reference
Class Field Theory by J.S. Milne.
Video Public
Yes
Notes Public
Yes
Lecturer Intro
Hu chuangqiang joined Bimsa in the autumn of 2021. The main research fields include: coding theory, function field and number theory, singularity theory. In recent years, he has made a series of academic achievements in the research of quantum codes, algebraic geometric codes, Drinfeld modules, elliptic singular points, Yau Lie algebras and other studies. He has published 13 papers in famous academic journals such as IEEE Trans. on IT., Final Fields and their Applications, Designs, Codes and Cryptography. He has been invited to attend domestic and international academic conferences for many times and made conference reports.