Instructor: 
Nils Bruin
nbruin@sfu.ca
SC K 10507
(778) 782 3794

Webpage: 
http://www.cecm.sfu.ca/~nbruin/math894EC 
Textbook:

 Silverman, Joseph H. The arithmetic of elliptic curves.
Graduate Texts in Mathematics, 106. SpringerVerlag, New York, 1986.
xii+400 pp. ISBN: 0387962034
 Silverman, Joseph H. Advanced topics in the arithmetic of elliptic curves.
Graduate Texts in Mathematics, 151. SpringerVerlag, New York, 1994.
xii+400 pp. ISBN: 0387943285

Pre/corequisite:

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 guideline, should prepare a lecture of about an hour. Our time slot
allows for overrun and discussion.

Grading: 
Lectures:  60% 
Assignments:  20% 
Participation:  20% 

Lecture schedule: 
Date 
Lecturer 
Title 
Sections 
Sep. 11 
Nils 
Planning and Introduction 
II 
Sep. 18 
Brett 
Introduction to elliptic curves 
III.13,5 
Sep. 25 
Parinaz 
Isogenies 
III.4,6 
Oct. 2 
Avi 
Tate module, Weil pairing and the endomorphism ring 
III.710 
Oct. 7 (extra, 9:30am) 
Avi 
Weil pairing and the endomorphism ring (continued) 
III.710 
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 MordellWeil Theorem 
VIII.14 
Nov. 13 
Parinaz 
Heights; Canonical height 
VIII.59 
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 MordellWeil group
 Elliptic surfaces
 Neron models of elliptic curves
