Mathematics 207a

Number Theory

Elliptic curves and Modular forms

Fall Quarter 2009

Haruzo HIDA

Meeting Time: Mondays and Wednesdays 12:00noon to 1:50pm in MS 6221
Office hours: before class meetings, from 11:00am and after class meeting from 2:00pm to 3:00pm (all Mondays) in my office: MS6308.

Texts: Lecture notes will be posted:
The notes of lectures [pdf] (some errors corrected on 12/1).

Though the treatment in my course will be far more elementary, as a reference book, we list my book
"Geometric Modular Forms and Elliptic Curves" WSPC, 2000

Topics: We assume Riemann-Roch theorem and Bezout theorem for general plane curves (though we state the theorem and explain its meaning in the course). Then, starting with basics of elliptic curves, I hope to touch the following topics in this course:

Proofs are often given limiting to elliptic curves defined over fields (possibly algebraically closed fields) as in published texts other than my book. But I will try to state theorems in general setting of elliptic curves defined over commutative rings and explain their meaning (proofs in the general case can be found in my book).

Prerequisite:
Good understanding of the material covered by the graduate course 210 (new) series (as listed in the outline of the algebra qualifying exam [qual outline]), some understanding of algebraic geometry and algebraic number theory will help.

Homework.
I would assign exercises in the lecture notes as homework, and possibly bring-back exam would be posted here (at the end of the course). The course grade is assigned by homework and exam performance.