Lecture Notes

1 Absolute values and discrete valuations (PDF)
2 Localization and Dedekind domains (PDF)
3 Properties of Dedekind domains, ideal class groups, factorization of ideals (PDF)
4 Étale algebras, norm and trace (PDF)
5 Dedekind extensions (PDF)
6 Ideal norms and the Dedekind-Kummer thoerem (PDF)
7 Galois extensions, Frobenius elements, and the Artin map (PDF)
8 Complete fields and valuation rings (PDF)
9 Local fields and Hensel's lemmas (PDF)
10 Extensions of complete DVRs (PDF)
11 Totally ramified extensions and Krasner's lemma (PDF)
12 The different and the discriminant (PDF)
13 Global fields and the product formula (PDF)
14 The Minkowski bound and finiteness results (PDF)
15 Dirichlet's unit theorem (PDF)
16 Riemann's zeta function and the prime number theorem (PDF)
17 The functional equation (PDF)
18 Dirichlet L-functions and primes in arithmetic progressions (PDF)
19 The analytic class number formula (PDF)
20 The Kronecker-Weber theorem (PDF)
21 Class field theory: ray class groups and ray class fields (PDF)
22 The main theorems of global class field theory (PDF)
23 Tate cohomology (PDF)
24 Artin reciprocity in the unramified case (PDF)
25 The ring of adeles, strong approximation (PDF)
26 The idele group, profinite groups, infinite Galois theory (PDF)
27 Local class field theory (PDF)
28 Global class field theory and the Chebotarev density theorem (PDF)