Mon 1/13
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introduction, various definitions for elliptic curves |
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1/13 to 1/15
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| Wed 1/15 |
the Mordell–Weil group |
[C] §7, |
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| Fri 1/17 |
algebraic sets, algebraic varieties, and dimension |
[S1] ch. I-II |
1/17 to 1/24 |
| Wed 1/22 |
singularities, rational maps and morphisms |
[S1] ch. I |
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| Fri 1/24 |
valuations, maps on function fields, ramification |
[S1] ch. II |
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| Mon 1/27 |
divisors and differentials |
[S1] ch. II |
1/27 to 1/31 |
| Wed 1/29 |
more divisors and differentials |
[S1] ch. II |
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Fri 1/31
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Riemann–Roch, Weierstrass equations and genus 1 |
[S1] ch. II, ch. III §3
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Mon 2/3
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Riemann–Hurwitz, various Weierstrass equations
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[S1] ch. II, ch. III §1
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2/3 to 2/7
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| Wed 2/5 |
j-invariants, singular Weierstrass cubics |
[S1] ch. III §1-2 |
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| Fri 2/7 |
the algebraic group law |
[S1] ch. III §3 |
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Mon 2/10
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isogenies
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[S1] ch. III §4
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2/10 to 2/17
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| Wed 2/12 |
invariant differential |
[S1] ch. III §5 |
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| Fri 2/14 |
dual isogeny |
[S1] ch. III §6 |
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| Mon 2/17 |
dual isogeny, applications to torsion |
[S1] ch. III §6 |
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| Wed 2/19 |
Tate module, Galois representations |
[S1] ch. III §7 |
2/19 |
Fri 2/21
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The Weil pairing
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[S1] ch. III §8
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2/21 to 2/26
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| Mon 2/24 |
Weil pairing on Tate module, applications |
[S1] ch. III §8 |
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| Wed 2/26 |
Endomorphisms |
[S1] ch. III §9-10 |
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| Fri 2/28 |
Endomorphisms in positive characteristic |
[S1] ch. V §3 |
2/28 and 3/5 |
Mon 3/3
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Elliptic curves over \(\mathbb{C}\)
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[S1] ch. VI, [S2] ch. I |
recording, notes |
| Wed 3/5 |
Hasse bound, Weil conjectures |
[S1] ch. V §1-2 |
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| Fri 3/7 |
Over local fields: reduction and torsion |
[S1] ch. VII §1-3 |
3/7 to 3/10 |
| Mon 3/10 |
Action of inertia, reduction types |
[S1] ch. VII §4-5 |
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| Wed 3/12 |
Weak Mordell–Weil pt 1 |
[S1] ch. VIII §1 |
3/12 to 3/17 |
| Fri 3/14 |
no class |
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| Mon 3/17 |
Weak Mordell–Weil pt 2, Descent Theorem |
[S1] ch. VIII §1, 3 |
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| Wed 3/19 |
Mordell’s Theorem, heights on \(\mathbb{P}^N\) |
[S1] ch. VIII §4, 5 |
3/19 to 3/21 |
| Fri 3/21 |
More heights |
[S1] ch. VIII §5 |
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| Spring Break |
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| Mon 3/31 |
Heights on elliptic curves (finishing MW!) |
[S1] ch. VIII §6 |
3/31 |
| Wed 4/2 |
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| Fri 4/4 |
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| Mon 4/7 |
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| Wed 4/9 |
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| Fri 4/11 |
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| Mon 4/14 |
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| Wed 4/16 |
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| Fri 4/18 |
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| Mon 4/21 |
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| Wed 4/23 |
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| Fri 4/25 |
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| Mon 4/28 |
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| Wed 4/30 |
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| Fri 5/2 |
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