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Last updated:

September 23, 2023

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Description

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)

Course Curriculum

  • 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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