| Instructor: |
Nils Bruin
nbruin@sfu.ca
SC K 10507
(778) 782 3794
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| Webpage: |
http://www.cecm.sfu.ca/~nbruin/math894EC |
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Textbook:
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- Silverman, Joseph H. The arithmetic of elliptic curves.
Graduate Texts in Mathematics, 106. Springer-Verlag, New York, 1986.
xii+400 pp. ISBN: 0-387-96203-4
- Silverman, Joseph H. Advanced topics in the arithmetic of elliptic curves.
Graduate Texts in Mathematics, 151. Springer-Verlag, New York, 1994.
xii+400 pp. ISBN: 0-387-94328-5
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Pre/corequisite:
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MATH 818, Algebraic curves. A basic knowledge of algebraic number theory is also very useful. |
| Meetings: |
Thursday, 9:30 - 11:20, P 9318 (part of P 9309, next to AQ level stairs entrance)
First meeting September 11 |
| Goal and format: |
Each meeting, one of the participants will lecture on a part of the textbook.
We will fix the assignment of topics and the lecture schedule on the first
meeting.
Lecturers, as a guide-line, should prepare a lecture of about an hour. Our time slot
allows for overrun and discussion.
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| Grading: |
| Lectures: | 60% |
| Assignments: | 20% |
| Participation: | 20% |
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| Lecture schedule: |
| Date |
Lecturer |
Title |
Sections |
| Sep. 11 |
Nils |
Planning and Introduction |
II |
| Sep. 18 |
Brett |
Introduction to elliptic curves |
III.1-3,5 |
| Sep. 25 |
Parinaz |
Isogenies |
III.4,6 |
| Oct. 2 |
Avi |
Tate module, Weil pairing and the endomorphism ring |
III.7-10 |
Oct. 7
(extra, 9:30am) |
Avi |
Weil pairing and the endomorphism ring (continued) |
III.7-10 |
| Oct. 9 |
Brett |
Formal groups |
IV |
| Oct. 16 |
Colin |
Elliptic curves over finite fields |
V |
| Oct. 23 |
Parinaz |
Elliptic curves over C |
VI |
| Oct. 30 |
Avi |
Elliptic curves over local fields |
VII |
| Nov. 6 |
Brett |
Weak Mordell-Weil Theorem |
VIII.1-4 |
| Nov. 13 |
Parinaz |
Heights; Canonical height |
VIII.5-9 |
| Nov. 20 |
Avi |
Computing Selmer Groups |
X |
| Nov. 27 |
Possible topics include:
- Endomorphism rings of elliptic curves
- Elliptic curves over finite and local fields
- Elliptic curves over global fields
- Explicit computation of the Mordell-Weil group
- Elliptic surfaces
- Neron models of elliptic curves
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