| Instructor | Paul Vojta |
|---|---|
| Lectures | TTh 12:30–2:00, Evans 47 |
| Class Number | 25377 |
| Office | 883 Evans |
| E-Mail: | vojta@math.berkeley.edu |
| Office Hours | TTh 11–12:30 excluding university holidays. Please email me to set up a time to meet if you cannot make any of these times. |
| Prerequisites | Math 254A and 256A; 256B or current enrollment in 256B may be required |
| Required Text | None |
| 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. |
| 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. | Date | Title | Download | |
|---|---|---|---|---|
| 1 | January 22 | Solution to Hartshorne II Ex. 3.15 | download | |
| 2 | January 24 | Nonsingular projective curves and their function fields | dvi | |
| 3 | January 29 | Chapter 0: Preliminary material (for reference only) | dvi | |
| 4 | January 29 | Chapter 1: Heights | dvi | |
| 5 | March 7 | Chapter 2: Weil function | dvi | |
| 6 | April 4 | Chapter 3: Models | ||
Solutions will be posted on bCourses after each assignment has been graded.
| No. | Due | Assignment | Notes | |
|---|---|---|---|---|
| 1 | 1/29 | dvi | ||
| 2 | 2/5 | dvi | Revised 1/31 | |
| 3 | 2/12 | dvi | ||
| 4 | 2/19 | dvi | ||
| 5 | 2/26 | dvi | Revised 2/21 | |
| 6 | 3/5 | dvi | Re-revised 3/1 | |
| 7 | 3/12 | dvi | ||
| 8 | 3/19 | dvi | ||
| 9 | 4/2 | dvi | ||
| 10 | 4/9 | dvi | Revised 4/4 | |
| 11 | 4/16 | dvi | Revised 4/11 | |
| 12 | 4/23 | dvi | Re-revised 4/19 | |
| 13 | 4/30 | dvi | ||
| 14 | 5/7 | dvi | ||
| 15 | Wednesday, 5/15 5pm | dvi | Revised 5/11 | |
Last updated 11 May 2019