MATH 894, Elliptic Curves (Reading Course)

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. Springer-Verlag, New York, 1986.
xii+400 pp. ISBN: 0-387-96203-4
Prerequisites: MATH 818, Algebraic curves. A basic knowledge of algebraic number theory is also very useful.
Meetings: Thursday, 10:30 - 12:20, K9509
First meeting January 15
Goal and format: The goal is that the participants learn about elliptic curves. As a specific goal, we will prove

Theorem (Mordell-Weil). Let E be an elliptic curve over a number field K. Then the set E(K) of K-rational points forms a finitely generated abelian group.

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, January 15.

Lecturers, as a guide-line, should prepare a lecture of about an hour. Our time slot allows for overrun and discussion.
Grading: Based on lectures and participation.
Lecture schedule:
Date Lecturer Title Sections
Jan 15 Nils Bruin Planning and Introduction I will sketch an outline of the lecture schedule and we will fill it in.
Jan 22 Himadri Ganguli Isogenies (III.4,5,6)
Jan 29 Kevin Doerksen The Tate module and the Weil Pairing (III.7,8)
Feb 5 Jim Parks Formal groups in general (IV.2-5)
Feb 12 Jim Parks Elliptic curves over local fields (IV.1,6 and VII. The real goals here are IV.3.2, IV.6.4 and IV.6.5)
Feb 19 Hui Yi Lu Elliptic curves over finite fields (V. 1.1 is particularly useful. Perhaps side-step to Lenstra Elliptic Curve Method for factorization of integers.)
Feb 26 Alexander Molnar Elliptic curves over C (VI. Theorem 6.1 is the goal)
Mar 5 Alexander Molnar Heights on Projective Space and the Mordell-Weil Theorem (VIII.3-5)
Mar 12 Nils Bruin The weak Mordell-Weil Theorem (See X.1.4 for an explicit example. For the rest, we'll follow another source)
Mar 19 ... ... ...