| # |
Date |
Topic (references) |
Materials |
| 1 | 2/7 | Tate's theorem | notes |
| 2 | 2/12 | Galois cohomology and the invariant map for local fields | notes |
| 3 | 2/14 | Proof of local Artin reciprocity | notes |
| 4 | 2/19 | Lubin-Tate formal groups | notes |
| 5 | 2/21 | Proof of the local existence theorem | notes |
| 6 | 2/26 | Automorphisms of the upper half plane | Miyaki 1.1-1.3 |
| 7 | 2/28 | Hyperbolic goemetry and Fuchsian groups | Miyaki 1.4-1.5 |
| 8 | 3/5 | Dirichlet domains and quotient spaces | Miyaki 1.6-1.7 |
| 9 | 3/7 | Riemann surfaces, Siegel's theorem | Miyaki 1.8-1.9 |
| 10 | 3/12 | Automorphic forms | Miyaki 2.1 |
| 11 | 3/14 | Forms with character, Petersson inner product, meromorphic differentials | Miyaki 2.2-2.3, Diamond-Shurman 3.3 |
| 12 | 3/19 | Genus and volume formulas | Miyaki 2.3-2.4 |
| 13 | 3/21 | Dimension formulas and Poincare series | Miyaki 2.5-2.6, Diamond-Shurman 4.2 |
| 14 | 4/2 | Hecke algebras | Miyaki 2.7-2.8 |
| 15 | 4/4 | Modular groups | Miyaki 4.1,4.2 |
| 16 | 4/9 | Hecke algebras for modular groups | Miyaki 4.5 |
| 17 | 4/11 | Eigenforms | Miyaki 4.5-4.6 |
| 17 | 4/18 | Primitive forms | Miyaki 4.6 |
| 18 | 4/23 | Elliptic curves, L-functions, analytic continuation and functional equation | Miyaki 4.3 |
| 19 | 4/25 | Abelian variaeties and Jacobians | Diamond-Shurman 6.1, 6.2 |
| 20 | 4/30 | Modular curves as moduli spaces, Hecke correspondences | Ribet-Stein 5,11,12 |
| 21 | 5/2 | Hecke operators on modular Jacobians, algebraic eigenvalues | Diamond-Shurman 6.3, 6.5 |
| 22 | 5/7 | Abelian varieties associated to Eigenforms | Diamond-Shurman 6.6, 7.7-9 |
