| # |
Date |
Topic (references) |
Materials |
| 1 | 9/10 | Absolute values and discrete valuations | notes |
| 2 | 9/15 | Localization and Dedekind domains | notes |
| 3 | 9/17 | Unique factorization of ideals in Dedekind domains, approximation | notes |
| 4 | 9/22 | Étale algebras, norm and trace, Dedekind extensions | notes |
| 5 | 9/24 | Factoring primes in Dedekind extensions | notes |
| 6 | 9/29 | Ideal norms and the Dedekind-Kummer thoerem | notes |
| 7 | 10/1 | Orders in Dedekind domains, primes in Galois extensions | notes |
| 8 | 10/6 | Frobenius elements, the Artin map, completions | notes |
| 9 | 10/9 | Local fields and extensions of complete DVRs | notes |
| 10 | 10/15 | Extensions of complete DVRs | notes |
| 11 | 10/20 | Completing extensions, different and discriminant ideals | notes |
| 12 | 10/22 | Ramification, Haar measure, the product formula | notes |
| 13 | 10/27 | The Minkowski bound, finiteness results | notes |
| 14 | 10/29 | Dirichlet's unit theorem | notes |
| 15 | 11/03 | The Riemann zeta function and the Prime Number Theorem | notes |
| 16 | 11/05 | The functional equation | notes |
| 17 | 11/10 | Dirichlet characters and primes in arithmetic progressions | notes |
| 18 | 11/12 | The analytic class number formula | notes |
| 19 | 11/17 | The Kronecker-Weber theorem | notes |
| 20 | 11/19 | Class field theory, ray class groups and ray class fields | notes |
| 21 | 11/24 | Statement of the main theorems of global class field theory | notes |
| 22 | 12/1 | The ring of adeles, strong approximation | notes |
| 23 | 12/3 | The idele group, profinite groups, infinite Galois theory | notes |
| 24 | 12/8 | Local class field theory | notes |
| 25 | 12/10 | Global class field theory and the Chebotarev density theorem | notes |
