Math 254B - Number Theory - Spring 2021

InstructorPaul Vojta
LecturesMWF 10:10–11:00, online
Class Number 24630
Office883 Evans
Office HoursTBD
PrerequisitesMath 254A and 256A
Required TextNone
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


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

No.DueAssignment Notes
12/3 dvi pdf
22/10 dvi pdf
32/19 dvi pdf
43/3 dvi pdf
53/18 dvi pdf
64/1 dvi pdf
74/13 dvi pdf
84/29 dvi pdf
95/13 dvi pdf

The following policies apply to the homework assignments.

  1. 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, accessed on 28 January 2013.)
  2. As an exception to the above, you may not collaborate on problems marked “(nc).”
  3. If you weren't able to do any exercise or part thereof, you may still assume that it holds for subsequent exercises or parts.
  4. 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