# |
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** |