18.785 - Number Theory I


# Date Topic (references) Materials
19/8Absolute values and discrete valuationsnotes
29/13Localization and Dedekind domainsnotes
39/15Properties of Dedekind domains, factorization of idealsnotes
49/20Étale algebras, norm and tracenotes
59/22Dedekind extensionsnotes
69/27Ideal norms, Dedekind-Kummer, orders, and conductorsnotes
79/29Galois extensions, Frobenius elements, the Artin mapnotes
810/4Complete fields and valuation ringsnotes
910/6Local fields and Hensel's lemmasnotes
1010/13Extensions of complete DVRsnotes
1110/18Totally ramified extensions and Krasner's lemmanotes
1210/20The different and the discriminantnotes
1310/25Global fields and the product formulanotes
1410/27The geometry of numbersnotes
1511/1Dirichlet's unit theoremnotes
1611/3Riemann's zeta function and the prime number theoremnotes
1711/8The functional equationnotes
1811/10Dirichlet L-functions and primes in arithmetic progressionsnotes
1911/15The analytic class number formulanotes
2011/17The Kronecker-Weber theoremnotes
2111/22Class field theory: ray class groups and ray class fieldsnotes
2211/24The main theorems of global class field theorynotes
23bonusTate cohomologynotes
24bonusArtin reciprocity (unramified case)notes
2511/29The ring of adeles, strong approximationnotes
2612/1The idele group, profinite groups, infinite Galois theorynotes
2712/6Local class field theorynotes
2812/8Global class field theory and the Chebotarev density theoremnotes