General Information
| Time |
MWF, 11:15 a.m. -- 12:05 p.m. |
| Location | Vincent Hall, Room 207 |
| Professor |
Ben Brubaker (brubaker@math.umn.edu)
Office: Vincent Hall, Room 352
Office Phone: TBD
Office Hours: W 1:30-2:30, Th 1:30-3:30, and always available by appointment |
| Textbook | Jürgen Neukirch, Algebraic Number Theory (Springer-Verlag) |
Course
Assignments | Problem sets every fortnight |
| Rough Syllabus | Chapters I, II, and the first three sections of Ch. III in Neukirch's book. We will finish with the statements of local and global class field theory, time permitting. |
Section and page numbers with an (N) denote Neukirch's book.
- Problem Set 1 (due Friday, September 19):
- N I.1 4,5,6,7
- N I.2 4,5,6 (in 5 and 6, "integral basis of" means integral basis of the ring of integers)
- N I.3 1,2,5,6
- Problem Set 2 (due Friday, October 3):
- N I.4 2
- N I.5 1
- N I.6 1,4,5,7
- N I.7 1,2,4,5
- Problem Set 3 (due Friday, October 17):
- N I.8 2, 5, 9
- N I.9 1, 2
- N I.10 1, 2, 3
- N I.11 1, 2
- N I.12 1
- Problem Set 4 (due Friday, November 7):
- N II.1 1, 2, 3, 5
- N II.2 2, 3, 5, 6, 7
- N II.3 1, 2, 3
- N II.4 2, 3, 4, 5, 6
- Problem Set 5 (due Monday, November 24):
- N II.5 2, 3, 4
- N II.6 5
- N II.7 1, 2, 3
- Problem Set 6 (due Wednesday, December 10):
- Weekly problem set solutions to appear here
- In an article in the Bulletin of the AMS from 1984,Steve Gelbart provides an overview of the Langlands Program to date. The article discusses many of the topics we hope to hint at over the year-long course, and provides historical motivation for our proposed route through algebraic number theory:
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