Wenhan Dai

Algebraic Number Theory 2 / 代数数论 2

2023 Fall, at Tsinghua University.

News & Announcements

[IMPORTANT] The final exam will take place in 6B204 at Jan 3, 2024. It is necessary to attend the exam for passing the course.

Course Logistics

The course is a continuation of Algebra and Number Theory 1, and it covers Class Field Theory. It plays a fundamental role in many branches of modern Number Theory, and thus it is one of the standard topics for Ph.D. students in the field. The course teaches the statements and proofs of Local and Global Class Field Theories. Along the way, we also discuss group cohomology and other related topics. Students will learn the course materials by attending lectures by the instructor and doing homework on a regular basis.

Instructor: Koji Shimizu (Shuangqing Complex Building B621).
Teaching Asistant: Wenhan Dai.
Time: 8-9:35 am on Wednesdays; 1:30-3:05 pm on Fridays.
Venue: 6B204 in No. 6 Teaching Building.
Prerequisites: Algebra and Number Theory 1.

Grading

Grading: First Problem Set 20%, Second Problem Set 20%, Final Exam 60%.
Homework: Homework consists of weekly reading assignments and two problem sets. The first problem set is due on October 31 and the second is due on December 5. The problems will be posted online two weeks before the deadline. No late submission will be accepted.
Final Exam: The final exam is cumulative and closed-book.
Attendance: You are expected to come prepared and actively participate in every lecture.

Office Hours

Instructor’s Office Hours: 2-3 p.m. on Thursdays in Shuangqing Complex Building B621 (tentative).
TA’s Office Hours: TBA. There will be extra office hours before the two homework submission deadlines.

Problem Sets

Problem Set 1 (due on Oct 31, see solutions).
Problem Set 2 (due on Dec 19, see solutions).

Final Exam

Problems with Solutions (note that the solution to 2(e) is corrected).

References

[AT09] Emil Artin and John Tate, Class field theory, AMS Chelsea Publishing, Providence, RI, 2009, Reprinted with corrections from the 1967 original.
[CF10] J. W. S. Cassels and A. Fröhlich (eds.), Algebraic number theory, London Mathematical Society, London, 2010, Papers from the conference held at the University of Sussex, Brighton, September 1–17, 1965, Including a list of errata.
[Mil20] J. S. Milne, Class Field Theory, 2020, Available here.
[Ser79] Jean-Pierre Serre, Local fields, Graduate Texts in Mathematics, vol. 67, Springer-Verlag, New York-Berlin, 1979, Translated from the French by Marvin Jay Greenberg.

Last updated on: January 4, 2024