| # |
Date |
Topic (references) |
Materials |
| 1 | 9/5 | Absolute values and discrete valuations | notes |
| 2 | 9/10 | Localization and Dedekind domains | notes |
| 3 | 9/12 | Properties of Dedekind domains, ideal class groups, factorization of ideals | notes |
| 4 | 9/17 | Étale algebras, norm and trace | notes |
| 5 | 9/19 | Dedekind extensions | notes |
| 6 | 9/24 | Ideal norms and the Dedekind-Kummer thoerem | notes |
| 7 | 9/26 | Galois extensions, Frobenius elements, the Artin map | notes |
| 8 | 10/1 | Complete fields and valuation rings | notes |
| 9 | 10/3 | Local fields and Hensel's lemmas | notes |
| 10 | 10/10 | Extensions of complete DVRs | notes |
| 11 | 10/15 | Totally ramified extensions and Krasner's lemma | notes |
| 12 | 10/17 | The different and the discriminant | notes |
| 13 | 10/22 | Global fields and the product formula | notes |
| 14 | 10/24 | Minkowski bound, finiteness results | notes |
| 15 | 10/29 | Dirichlet's unit theorem | notes |
| 16 | 10/31 | Riemann's zeta function and the prime number theorem | notes |
| 17 | 11/5 | The functional equation | notes |
| 18 | 11/7 | Dirichlet L-functions and primes in arithmetic progressions | notes |
| 19 | 11/14 | The analytic class number formula | notes |
| 20 | 11/19 | The Kronecker-Weber theorem | notes |
| 21 | 11/21 | Class field theory: ray class groups and ray class fields | notes |
| 22 | 11/26 | The main theorems of global class field theory | notes |
| 23 | 11/28 | (Optional) Tate cohomology | notes |
| 24 | 11/28 | (Optional) Artin reciprocity (unramified case) | notes |
| 25 | 11/28 | The ring of adeles, strong approximation | notes |
| 26 | 12/3 | The idele group, profinite groups, infinite Galois theory | notes |
| 27 | 12/5 | Local class field theory | notes |
| 28 | 12/10 | Global class field theory and the Chebotarev density theorem | notes |
