| # |
Date |
Topic (references) |
Materials |
| 1 | 9/5 | Introduction to arithmetic geometry (Ellenberg, Poonen) | slides, worksheet |
| 2 | 9/10 | Rational points on conics (Cremona-Rusin) | notes |
| 3 | 9/12 | Finite fields (Rabin) | notes, worksheet |
| 4 | 9/17 | The ring of p-adic integers | notes |
| 5 | 9/19 | The field of p-adic numbers, absolute values, Ostrowski's theorem for Q | notes |
| 6 | 9/24 | Ostrowski's theorem for number fields (Conrad) | |
| 7 | 9/26 | Product formula for number fields, completions | notes |
| 8 | 10/1 | Hensel's lemma | notes |
| 9 | 10/3 | Quadratic forms | notes |
| 10 | 10/8 | Hilbert symbols | notes |
| 11 | 10/10 | Weak and strong approximation, Hasse-Minkowski theorem for Q | notes |
| 12 | 10/17 | Field extensions, algebraic sets | notes |
| 13 | 10/22 | Affine and projective varieties | notes |
| 14 | 10/24 | Zariski topology, morphisms of affine varieties and affine algebras | notes |
| 15 | 10/29 | Rational maps and function fields | notes |
| 16 | 10/31 | Products of varieties and Chevalley's criterion for completeness | notes |
| 17 | 11/5 | Tangent spaces, singular points, hypersurfaces | notes |
| 18 | 11/7 | Smooth projective curves | notes |
| 19 | 11/12 | Divisors, the Picard group | notes |
| 20 | 11/14 | Degree theorem for morphisms of curves | notes |
| 21 | 11/19 | Riemann-Roch spaces | notes |
| 22 | 11/21 | Proof of the Riemann-Roch theorem for curves | notes |
| 23 | 11/26 | Elliptic curves and abelian varieties | notes |
| 24 | 12/3 | Isogenies and torsion points, the Nagell-Lutz theorem | notes |
| 25 | 12/5 | The Mordell-Weil theorem | notes |
| 26 | 12/10 | Jacobians of genus one curves, the Weil-Chatelet and Tate-Shafarevich groups | notes |
