Course Identification

Class field theory
20194072

Lecturers and Teaching Assistants

Prof. Dmitry Gourevitch, Prof. Joseph Bernstein
N/A

Course Schedule and Location

2019
Second Semester
Monday, 13:15 - 14:00, Ziskind, Rm 1
Tuesday, 14:15 - 16:00, Jacob Ziskind Building, Rm 155
25/03/2019

Field of Study, Course Type and Credit Points

Mathematics and Computer Science: Seminar; Elective; Regular; 3.00 points

Comments

N/A

Prerequisites

Knowledge of basic facts about global and local fields (a basic course in algebraic number theory is enough).

Representations of finite groups. Some complex analysis.

Restrictions

30

Language of Instruction

English

Attendance and participation

Expected and Recommended

Grade Type

Pass / Fail

Grade Breakdown (in %)

30%
70%

Evaluation Type

Seminar

Scheduled date 1

N/A
N/A
-
N/A

Estimated Weekly Independent Workload (in hours)

9

Syllabus

  1. Relations beteen local and global Galois groups.
  2. Examples of explicit constructions in Class Field Theory (CFT).
  3. Global characterization of the Artin map.
  4. Neikrich's local characterization of Artin map.
  5. Lubin-Tate construction.
  6. Galois cohomologiy and CFT.
  7. L-functions, densities of primes.
  8. Statement and proof of global CFT.

Learning Outcomes

Upon successful completion of this course , the students will able to:

  1. Demonstrate knowledge of the basics of class field theory, that lies in the basis of the Langlands program and of the modern algebraic number theory. 
  2. Describe one-dimensional representations of the absolute Galois group of global fields (i.e. algebraic extensions of Q) and local fields (i.e. algebraic esxtensions of completions of Q).

Reading List

1. Lang's book "Algebraic number theory".

2. TBA

Website