Math 254B - Number Theory

InstructorPaul Vojta
LecturesTTh 12:30–2:00, Evans 47
Class Number25377
Office883 Evans
E-Mail:vojta@math.berkeley.edu
Office HoursTTh 11–12:30
excluding university holidays.
Please email me to set up a time to meet if you cannot make any of these times.
PrerequisitesMath 254A and 256A; 256B or current enrollment in 256B may be required
Required TextNone
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 the more advanced topic of Arakelov theory, including applications to diophantine problems.
GradingGrades 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.DateTitle Download
1January 22 Solution to Hartshorne II Ex. 3.15 download
2January 24 Nonsingular projective curves and their function fields dvi pdf
3January 29 Chapter 0: Preliminary material (for reference only) dvi pdf
4January 29 Chapter 1: Heights dvi pdf
5March 7 Chapter 2: Weil function dvi pdf
6April 4 Chapter 3: Models pdf

Homework Assignments

Solutions will be posted on bCourses after each assignment has been graded.

No.DueAssignment Notes
11/29 dvi pdf
22/5 dvi pdfRevised 1/31
32/12 dvi pdf
42/19 dvi pdf
52/26 dvi pdfRevised 2/21
63/5 dvi pdfRe-revised 3/1
73/12 dvi pdf
83/19 dvi pdf
94/2 dvi pdf
104/9 dvi pdfRevised 4/4
114/16 dvi pdfRevised 4/11
124/23 dvi pdf Re-revised 4/19
134/30 dvi pdf
145/7 dvi pdf
15 Wednesday, 5/15 5pm dvi pdfRevised 5/11

Last updated 11 May 2019