18.785 - Number Theory I


SCHEDULE

# Date Topic (references) Materials
19/4Absolute values and discrete valuationsnotes
29/9Localization and Dedekind domainsnotes
39/11Properties of Dedekind domains, ideal class groups, factorization of idealsnotes
49/16Étale algebras, norm and tracenotes
59/18Dedekind extensionsnotes
69/23Ideal norms, Dedekind-Kummer, orders, and conductorsnotes
79/25Galois extensions, Frobenius elements, the Artin mapnotes
89/30Complete fields and valuation ringsnotes
910/2Local fields and Hensel's lemmasnotes
1010/7Extensions of complete DVRsnotes
1110/9Totally ramified extensions and Krasner's lemmanotes
1210/16The different and the discriminantnotes
1310/21Global fields and the product formulanotes
1410/23The geometry of numbersnotes
1510/28Dirichlet's unit theoremnotes
1610/30Riemann's zeta function and the prime number theoremnotes
1711/4The functional equationnotes
1811/6Dirichlet L-functions and primes in arithmetic progressionsnotes
1911/13The analytic class number formulanotes
2011/18The Kronecker-Weber theoremnotes
2111/20Class field theory: ray class groups and ray class fieldsnotes
2211/25The main theorems of global class field theorynotes
2311/27Tate cohomologynotes
2411/27Artin reciprocity (unramified case)notes
2512/2The ring of adeles, strong approximationnotes
2612/4The idele group, profinite groups, infinite Galois theorynotes
2712/9Local class field theorynotes
2812/11Global class field theory and the Chebotarev desnity theoremnotes