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Class Field Theory
Math 582 H; Winter 2016

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Lecture: MWF 2:30 - 3:50, Art Building 006
Office Hours: TBD

Course Outline: We will cover the main statements of class field theory (both local and global). If time permits, we will cover the proofs of local class field theory and give an overview of the proofs of global class field theory. The last few classes will be devoted to student presentations which will mainly focus on applications of class field theory.

References and expository articles:

1. Class Field Theory: The Bonn Lectures by Neukirch
2. Class Field Theory by Milne
3. Number Theory 2: Introduction to Class Field Theory by Kato, Kurokawa, and Saito
4. Algebraic Number Theory by Cassels and Fröhlich
5. History of Class Field Theory by K. Conrad
6. A brief summary of the statements of Class Field Theory by Poonen
7. An overview of Class Field Theory by Shemanske
8. What is a reciprocity law? by Wyman

Project: Each student will prepare a 30 minute presentation as well as an 5-10 page accompanying writeup. I will provide a list of suggested topics; students are also welcome to come up with their own topic. Topics should be finalized by Monday, February 11 (if not earlier), presentations should be ready by Wednesday, February 3, and papers are due by email on Friday, March 11.

Exercises: The following exercises may be useful in solidifying the concepts from class; they are not required.

1. Homework assignments from Brian Conrad's class on Class Field Theory
2. Exercises from Cassels and Fröhlich
3. Exercises from Class Field Theory by Milne