| LEC # | TOPICS | KEY DATES |
|---|---|---|
| 1 | Introduction to Arithmetic Geometry | |
| 2 | Rational Points on Conics | |
| 3 | Finite Fields | |
| 4 | The Ring of p-adic Integers | Problem Set 1 Due |
| 5 | The Field of p-adic Numbers, Absolute Values, Ostrowski's Theorem for Q | |
| 6 | Ostrowski's Theorem for Number Fields | Problem Set 2 Due |
| 7 | Product Formula for Number Fields, Completions | |
| 8 | Hensel's Lemma | Problem Set 3 Due |
| 9 | Quadratic Forms | |
| 10 | Hilbert Symbols | Problem Set 4 Due |
| 11 | Weak and Strong Approximation, Hasse-Minkowski Theorem for Q | |
| 12 | Field Extensions, Algebraic Sets | |
| 13 | Affine and Projective Varieties | Problem Set 5 Due |
| 14 | Zariski Topology, Morphisms of Affine Varieties and Affine Algebras | |
| 15 | Rational Maps and Function Fields | Problem Set 6 Due |
| 16 | Products of Varieties and Chevalley's criterion for Completeness | |
| 17 | Tangent Spaces, Singular Points, Hypersurfaces | Problem Set 7 Due |
| 18 | Smooth Projective Curves | |
| 19 | Divisors, The Picard Group | Problem Set 8 Due |
| 20 | Degree Theorem for Morphisms of Curves | |
| 21 | Riemann-Roch Spaces | |
| 22 | Proof of the Riemann-Roch Theorem for Curves | Problem Set 9 Due |
| 23 | Elliptic Curves and Abelian Varieties | |
| 24 | Isogenies and Torsion Points, The Nagell-Lutz Theorem | Problem Set 10 Due |
| 25 | The Mordell-Weil Theorem | |
| 26 | Jacobians of Genus One Curves, The Weil-Chatelet and Tate-Shafarevich Groups | Problem Set 11 Due |