Math 254B - Number Theory - Spring 2021

Instructor	Paul Vojta
Lectures	MWF 10:10–11:00, online
Class Number	24630
Office	883 Evans
E-Mail:	`vojta@math.berkeley.edu`
Office Hours	TBD
Prerequisites	Math 254A and 256A
Required Text	None
Catalog Description	Math 254AB: 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 the more advanced topic of Arakelov theory, including applications to diophantine problems.
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

Handouts

No.	Date	Title	Download
1	January 22	Solution to Hartshorne II Ex. 3.15	download
2	January 29	Nonsingular projective curves and their function fields	dvi	pdf
3	February 6	Chapter 0: Preliminary material (for reference only) (revised 2/13)	dvi	pdf
4	February 13	Chapter 1: Heights	dvi	pdf
5	March 1	Chapter 2: Weil functions	dvi	pdf
6	March 8	Pull-backs of line bundles and rational sections	dvi	pdf
7	March 29	Chapter 3: Models	pdf

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	2/10	dvi	pdf
3	2/19	dvi	pdf
4	3/3	dvi	pdf
5	3/18	dvi	pdf
6	4/1	dvi	pdf
7	4/13	dvi	pdf
8	4/29	dvi	pdf
9	5/13	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).”
If you weren't able to do any exercise or part thereof, 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).

Last updated 6 May 2021