| 1 |
Introduction to Arithmetic Geometry (PDF), 18.782 Lecture 1 (SWS)
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| 2 | Rational Points on Conics (PDF) |
| 3 |
Finite Fields (PDF), 18.782 Lecture 3 (SWS)
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| 4 | The Ring of p-adic Integers (PDF) |
| 5 | The Field of p-adic Numbers, Absolute Values, Ostrowski's Theorem for Q (PDF) |
| 6 | Ostrowski's Theorem for Number Fields (No lecture notes but see  Ostrowski's Theorem for Number Fields (PDF) by Keith Conrad) |
| 7 | Product Formula for Number Fields, Completions (PDF) |
| 8 | Hensel's Lemma (PDF) |
| 9 | Quadratic Forms (PDF) |
| 10 |
Hilbert Symbols (PDF), 18.782 Lecture 10 (SWS)
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| 11 | Weak and Strong Approximation, Hasse-Minkowski Theorem for Q (PDF) |
| 12 | Field Extensions, Algebraic Sets (PDF) |
| 13 | Affine and Projective Varieties (PDF) |
| 14 | Zariski Topology, Morphisms of Affine Varieties and Affine Algebras (PDF) |
| 15 | Rational Maps and Function Fields (PDF) |
| 16 | Products of Varieties and Chevalley's criterion for Completeness (PDF) |
| 17 | Tangent Spaces, Singular Points, Hypersurfaces (PDF) |
| 18 | Smooth Projective Curves (PDF) |
| 19 | Divisors, The Picard Group (PDF) |
| 20 | Degree Theorem for Morphisms of Curves (PDF) |
| 21 | Riemann-Roch Spaces (PDF) |
| 22 | Proof of the Riemann-Roch Theorem for Curves (PDF) |
| 23 | Elliptic Curves and Abelian Varieties (PDF) |
| 24 | Isogenies and Torsion Points, The Nagell-Lutz Theorem (PDF) |
| 25 | The Mordell-Weil Theorem (PDF) |
| 26 | Jacobians of Genus One Curves, The Weil-Chatelet and Tate-Shafarevich Groups (PDF) |
