Math 679: Elliptic Curves (Fall 2013, Open.Michigan) | Mathematics

Math 679: Elliptic Curves

Math 679: Elliptic Curves (Fall 2013, Open.Michigan). Instructor: Prof. Andrew Snowden. Math 679 is a graduate level mathematics course whose purpose is to prove Mazur's theorem. Mazur's theorem is a well-known and important result, however it is not often taught in classroom settings. The course is divided into three parts: elliptic curves and abelian varieties, moduli of elliptic curves, and proof of Mazur's theorem. (from open.umich.edu)

Overview

Lecture 01 - Overview

Lecture 02 - Elliptic Curves

Lecture 03 - Abelian Varieties (Analytic Theory)

Lecture 04 - Abelian Varieties (Algebraic Theory)

Lecture 05 - Group Schemes 1

Lecture 06 - Group Schemes 2

Lecture 07 - Raynaud's Theorem

Lecture 08 - Elliptic Curves over DVRs

Lecture 09 - Neron Models

Lecture 10 - Jacobians

Lecture 11 - Criterion for Rank 0

Lecture 12 - Modular Curves over C

Lecture 13 - Modular Forms

Lecture 14 - Modular Curves over Q

Lecture 15 - Modular Curves over Z

Lecture 16 - Structure of the Hecke Algebra

Lecture 17 - Eichler-Shimura

Lecture 18 - Criterion for Non-existence of Torsion Points

Lecture 19 - J₀(N) Mod N

Lecture 20 - Proof of Mazur's Theorem (Part 1)

Lecture 21 - Proof of Mazur's Theorem (Part 2)

Lecture 22 - 13 Torsion

Lecture 23 - Finishing Up

References

Math 679: Elliptic Curves
Instructor: Prof. Andrew Snowden. Course Materials. Math 679 is a graduate level mathematics course whose purpose is to prove Mazur's theorem.