18.786 - Number Theory I


# Date Topic (references) Materials
12/7Tate's theoremnotes
22/12Galois cohomology and the invariant map for local fieldsnotes
32/14Proof of local Artin reciprocitynotes
42/19Lubin-Tate formal groupsnotes
52/21Proof of the local existence theoremnotes
62/26Automorphisms of the upper half planeMiyaki 1.1-1.3
72/28Hyperbolic goemetry and Fuchsian groupsMiyaki 1.4-1.5
83/5Dirichlet domains and quotient spacesMiyaki 1.6-1.7
93/7Riemann surfaces, Siegel's theoremMiyaki 1.8-1.9
103/12Automorphic formsMiyaki 2.1
113/14Forms with character, Petersson inner product, meromorphic differentialsMiyaki 2.2-2.3, Diamond-Shurman 3.3
123/19Genus and volume formulasMiyaki 2.3-2.4
133/21Dimension formulas and Poincare seriesMiyaki 2.5-2.6, Diamond-Shurman 4.2
144/2Hecke algebrasMiyaki 2.7-2.8
154/4Modular groupsMiyaki 4.1,4.2
164/9Hecke algebras for modular groupsMiyaki 4.5
174/11EigenformsMiyaki 4.5-4.6
174/18Primitive formsMiyaki 4.6
184/23Elliptic curves, L-functions, analytic continuation and functional equationMiyaki 4.3
194/25Abelian variaeties and JacobiansDiamond-Shurman 6.1, 6.2
204/30Modular curves as moduli spaces, Hecke correspondencesRibet-Stein 5,11,12
215/2Hecke operators on modular Jacobians, algebraic eigenvaluesDiamond-Shurman 6.3, 6.5
225/7Abelian varieties associated to EigenformsDiamond-Shurman 6.6, 7.7-9