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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.