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Math 679: Elliptic Curves (Fall 2013, Open. Michigan). Instructor: Prof. Andrew Snowden.
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Description
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)
Course content
- Lecture 01 – Overview Unlimited
- Lecture 02 – Elliptic Curves Unlimited
- Lecture 03 – Abelian Varieties (Analytic Theory) Unlimited
- Lecture 04 – Abelian Varieties (Algebraic Theory) Unlimited
- Lecture 05 – Group Schemes 1 Unlimited
- Lecture 06 – Group Schemes 2 Unlimited
- Lecture 07 – Raynaud’s Theorem Unlimited
- Lecture 08 – Elliptic Curves over DVRs Unlimited
- Lecture 09 – Neron Models Unlimited
- Lecture 10 – Jacobians Unlimited
- Lecture 11 – Criterion for Rank 0 Unlimited
- Lecture 12 – Modular Curves over C Unlimited
- Lecture 13 – Modular Forms Unlimited
- Lecture 14 – Modular Curves over Q Unlimited
- Lecture 15 – Modular Curves over Z Unlimited
- Lecture 16 – Structure of the Hecke Algebra Unlimited
- Lecture 17 – Eichler-Shimura Unlimited
- Lecture 18 – Criterion for Non-existence of Torsion Points Unlimited
- Lecture 19 – J0(N) Mod N Unlimited
- Lecture 20 – Proof of Mazur’s Theorem (Part 1) Unlimited
- Lecture 21 – Proof of Mazur’s Theorem (Part 2) Unlimited
- Lecture 22 – 13 Torsion Unlimited
- Lecture 23 – Finishing Up Unlimited
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