|Lectures||MWF 10–11, Evans 736|
|Office Hours||MWF 11:30–12:30|
excluding non-instructional days.
Please email me to set up a time to meet if you cannot make any of these times.
|GSI Office Hours||The GSI for Math 254B is Rahul Dalal. He will hold office hours on MTuF 2–3 (omitting Wednesdays) and Thursdays 10–11 and 1–3, in 1041 Evans.|
|Required Text||J. Neukirch, Algebraic number theory, Springer, 2010|
|Catalog Description||Valuations, units, and ideals in number fields, ramification theory, quadratic and cyclotomic fields, topics from class field theory, zeta-functions and L-series, distribution of primes, modular forms, quadratic forms, diophantine equations, p-adic analysis, and transcendental numbers.|
|Syllabus||I plan to cover Class Field Theory, as given in Chapters IV–VI of the textbook.|
|Grading||Grades will be based on homework assignments, and possibly in-class quizzes. There will be no final exam, but the last problem set will be due sometime during the week of final exams.|
|Homework||Weekly or biweekly, assigned in class|
|1||January 27||Synopsis of class field theory||dvi|
Solutions will be posted on bCourses after each assignment has been graded.
To submit your assignments, use bCourses. I have set it to accept only pdf files.
|1||1/31||pp. 367–368: 3, 11, 12, 13.||For #3, If1 is defined in the proof of (1.11), and the completion of ℤ is defined on page 272 (Example 4).|
|2||2/7||p. 368: 14; p. 265: 4, 5; p. 274: 3(nc).||For the second problem, note that profinite group is defined on page 264.|
|3||2/14||dvi||Exercise 4 on page 290 is no longer assigned.|
|4||2/28||dvi||This replaces the earlier Homework 4, originally due on Feb. 21|
|5||3/6||p. 298–299: 1, 3||Hint for #1: Use the method of the proof of Proposition (5.5),
with one of the factors σi replaced by
an element of G(L-tilde/K-tilde).|
Also for #1: There's a sign error. Show instead that rL/K(σ)=N(y)-1.
|6||3/20||dvi||Correction (3/14): For the last question, assume that G is finite cyclic.|
The following policies apply to the homework assignments.
Last updated 27 March 2020