# |
Date |
Topic (references) |
Materials |

1 | 9/8 | Absolute values and discrete valuations | **notes** |

2 | 9/13 | Localization and Dedekind domains | **notes** |

3 | 9/15 | Properties of Dedekind domains, factorization of ideals | **notes** |

4 | 9/20 | Étale algebras, norm and trace | **notes** |

5 | 9/22 | Dedekind extensions | **notes** |

6 | 9/27 | Ideal norms, Dedekind-Kummer, orders, and conductors | **notes** |

7 | 9/29 | Galois extensions, Frobenius elements, the Artin map | **notes** |

8 | 10/4 | Complete fields and valuation rings | **notes** |

9 | 10/6 | Local fields and Hensel's lemmas | **notes** |

10 | 10/13 | Extensions of complete DVRs | **notes** |

11 | 10/18 | Totally ramified extensions and Krasner's lemma | **notes** |

12 | 10/20 | The different and the discriminant | **notes** |

13 | 10/25 | Global fields and the product formula | **notes** |

14 | 10/27 | The geometry of numbers | **notes** |

15 | 11/1 | Dirichlet's unit theorem | **notes** |

16 | 11/3 | Riemann's zeta function and the prime number theorem | **notes** |

17 | 11/8 | The functional equation | **notes** |

18 | 11/10 | Dirichlet L-functions and primes in arithmetic progressions | **notes** |

19 | 11/15 | The analytic class number formula | **notes** |

20 | 11/17 | The Kronecker-Weber theorem | **notes** |

21 | 11/22 | Class field theory: ray class groups and ray class fields | **notes** |

22 | 11/24 | The main theorems of global class field theory | **notes** |

23 | bonus | Tate cohomology | **notes** |

24 | bonus | Artin reciprocity (unramified case) | **notes** |

25 | 11/29 | The ring of adeles, strong approximation | **notes** |

26 | 12/1 | The idele group, profinite groups, infinite Galois theory | **notes** |

27 | 12/6 | Local class field theory | **notes** |

28 | 12/8 | Global class field theory and the Chebotarev density theorem | **notes** |