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 |