18.785 - Number Theory I


# Date Topic (references) Materials
19/6Absolute values and discrete valuationsnotes
29/11Localization and Dedekind domainsnotes
39/13Properties of Dedekind domains, ideal class groups, factorization of idealsnotes
49/18Étale algebras, norm and tracenotes
59/20Dedekind extensionsnotes
69/25Ideal norms and the Dedekind-Kummer thoeremnotes
79/27Galois extensions, Frobenius elements, the Artin mapnotes
810/2Complete fields and valuation ringsnotes
910/4Local fields and Hensel's lemmasnotes
1010/11Extensions of complete DVRsnotes
1110/16Totally ramified extensions and Krasner's lemmanotes
1210/19The different and the discriminantnotes
1310/25Global fields and the product formulanotes
1410/27Minkowski bound, finiteness resultsnotes
1510/30Dirichlet's unit theoremnotes
1611/3Riemann's zeta function and the prime number theoremnotes
1711/6The functional equationnotes
1811/10Dirichlet L-functions and primes in arithmetic progressionsnotes
1911/13The analytic class number formulanotes
2011/15The Kronecker-Weber theoremnotes
2111/20Class field theory: ray class groups and ray class fieldsnotes
2211/22The main theorems of global class field theorynotes
2311/27Tate cohomologynotes
2411/29Artin reciprocity (unramified case)notes
2512/4The ring of adeles, strong approximationnotes
2612/6The idele group, profinite groups, infinite Galois theorynotes
2712/8Local class field theorynotes
2812/13Global class field theory and the Chebotarev density theoremnotes