【椭圆曲线，模曲线与Mazur定理】【Michigian】Course on Mazur's theorem by Andrew Snowden
https://youtu.be/090K9XerdOU
Notes: http://www-personal.umich.edu/~asnowden/teaching/2013/679/index.html
Purpose is to prove Mazur's theorem on torsion in elliptic curves over \Q, and develop background on elliptic curves and their moduli.
视频选集
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Lecture 1 Overview
48:24
Lecture 2 Elliptic curves
01:17:24
Lecture 3 Abelian varieties (analytic theory)
01:20:41
Lecture 4 Abelian varieties (algebraic theory)
01:17:38
Lecture 5 Group schemes 1
01:21:03
Lecture 6 Group schemes 2
01:17:40
Lecture 7 Raynaud's theorem
01:16:46
Lecture 8 Elliptic curves over DVRs
01:14:13
Lecture 9 Néron models
01:12:12
Lecture 10 Jacobians
01:17:01
Lecture 11 Criterion for rank 0
01:11:23
Lecture 12 Modular curves over C
01:06:02
Lecture 13 Modular forms
01:20:53
Lecture 14 Modular curves over Q
01:19:42
Lecture 15 Modular curves over Z
01:08:31
Lecture 16 Structure of the Hecke algebra
01:05:42
Lecture 17 Eichler-Shimura
01:07:20
Lecture 18 Criterion for non-existence of torsion points
01:10:26
Lecture 19 J_0(N) mod N
01:18:53
Lecture 20 Proof of Mazur's theorem (part 1)
01:09:48
Lecture 21 Proof of Mazur's theorem (part 2)
01:11:48
Lecture 22 13 torsion
01:11:45
Lecture 23 Finishing up
51:58
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