Math 254B - Number Theory

Instructor	Paul Vojta
Lectures	MWF 10–11, Evans 3
Class Number	26320
Office	883 Evans
E-Mail:	`vojta@math.berkeley.edu`
Office Hours	M 11:30–12:30, W 11:10–12, F 11:30–12:30 excluding holidays and non-instructional days. Please email me to set up a time to meet if you cannot make any of these times.
Prerequisites	Math 254A
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. 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

Handouts

No.	Date	Title	Download
1	January 22	Synopsis of class field theory	dvi	pdf
2	April 14	An unexpectedly difficult lemma from class	dvi	pdf
3	April 21	Some details on the proof of VI (5.1)	dvi	pdf
3a	April 28	Some details on the proof of VI (5.1) (revised 4/28)	dvi	pdf

Homework Assignments

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.

If you type your homework on the computer (e.g., using LaTeX), then you should be able to create a pdf file directly on the computer and upload it.
If you handwrite your homework, you can use a scanner or your phone's camera to take pictures of your written work, then combine these images into a single PDF file with an app or website such as https://smallpdf.com/jpg-to-pdf.

No.	Due	Assignment
1	2/3	dvi	pdf
2	2/12	dvi	pdf
3	2/19	dvi	pdf
4	2/26	dvi	pdf
5	3/5	dvi	pdf
6	3/12	dvi	pdf
7	3/20	dvi	pdf
8	4/3	dvi	pdf
9	4/10	dvi	pdf
10	4/17	dvi	pdf
11	4/24	dvi	pdf
12	5/1	dvi	pdf
13	5/8	dvi	pdf
14	5/15	dvi	pdf

The following policies apply to the homework assignments.

Discussion and the exchange of ideas are essential to doing academic work. For assignments in this course, you are encouraged to consult with your classmates as you work on problem sets. However, after discussions with peers, make sure that you can work through the problem yourself and ensure that any answers you submit for evaluation are the result of your own efforts. In addition, you must cite any books, articles, websites, lectures, etc. that have helped you with your work using appropriate citation practices (other than class lectures and corresponding parts of the textbook). Similarly, you must list the names of students with whom you have collaborated on problem sets. (This paragraph was adapted from http://oue.fas.harvard.edu/icb/icb.do?keyword=k18059&pageid=icb.page498261, accessed on 28 January 2013.)
As an exception to the above, you may not collaborate on problems marked “(nc).”
For problems from the book, you may use without proof any lower-numbered exercises from the same section or any exercises from sections covered earlier. For other exercises, you may use without proof any exercises from earlier sections in the book; for the current section(s), ask. For any exercises, if you weren't able to do an exercise or part of an exercise, you may still assume that it holds for subsequent exercises or parts.
Credit may be reduced if you look up the answer in some other source (as opposed to using the material from elsewhere to aid in your understanding), or if you look ahead in the textbook.
Due to budget constraints, not all questions may be graded.

Last updated 8 May 2025