| # |
Date |
Topic (references) |
Materials |
| 1 | 9/4 | Absolute values and discrete valuations | notes |
| 2 | 9/9 | Localization and Dedekind domains | notes |
| 3 | 9/11 | Properties of Dedekind domains, ideal class groups, factorization of ideals | notes |
| 4 | 9/16 | Étale algebras, norm and trace | notes |
| 5 | 9/18 | Dedekind extensions | notes |
| 6 | 9/23 | Ideal norms, Dedekind-Kummer, orders, and conductors | notes |
| 7 | 9/25 | Galois extensions, Frobenius elements, the Artin map | notes |
| 8 | 9/30 | Complete fields and valuation rings | notes |
| 9 | 10/2 | Local fields and Hensel's lemmas | notes |
| 10 | 10/7 | Extensions of complete DVRs | notes |
| 11 | 10/9 | Totally ramified extensions and Krasner's lemma | notes |
| 12 | 10/16 | The different and the discriminant | notes |
| 13 | 10/21 | Global fields and the product formula | notes |
| 14 | 10/23 | The geometry of numbers | notes |
| 15 | 10/28 | Dirichlet's unit theorem | notes |
| 16 | 10/30 | Riemann's zeta function and the prime number theorem | notes |
| 17 | 11/4 | The functional equation | notes |
| 18 | 11/6 | Dirichlet L-functions and primes in arithmetic progressions | notes |
| 19 | 11/13 | The analytic class number formula | notes |
| 20 | 11/18 | The Kronecker-Weber theorem | notes |
| 21 | 11/20 | Class field theory: ray class groups and ray class fields | notes |
| 22 | 11/25 | The main theorems of global class field theory | notes |
| 23 | 11/27 | Tate cohomology | notes |
| 24 | 11/27 | Artin reciprocity (unramified case) | notes |
| 25 | 12/2 | The ring of adeles, strong approximation | notes |
| 26 | 12/4 | The idele group, profinite groups, infinite Galois theory | notes |
| 27 | 12/9 | Local class field theory | notes |
| 28 | 12/11 | Global class field theory and the Chebotarev desnity theorem | notes |
