LEC #
TOPICS
KEY DATES
1
Absolute Values and Discrete Valuations
2
Localization and Dedekind Domains
3
Properties of Dedekind Domains and Factorization of Ideals
Problem set 1 due
4
Étale Algebras, Norm and Trace
5
Dedekind Extensions
Problem set 2 due
6
Ideal Norms and the Dedekind-Kummer Theorem
7
Galois Extensions, Frobenius Elements, and the Artin Map
Problem set 3 due
8
Complete Fields and Valuation Rings
9
Local Fields and Hensel’s Lemmas
Problem set 4 due
10
Extensions of Complete DVRs
11
Totally Ramified Extensions and Krasner’s Lemma
12
The Different and the Discriminant
Problem set 5 due
13
Global Fields and the Product Formula
14
The Geometry of Numbers
Problem set 6 due
15
Dirichlet’s Unit Theorem
16
Riemann’s Zeta Function and the Prime Number Theorem
17
The Functional Equation
Problem set 7 due
18
Dirichlet L-functions and Primes in Arithmetic Progressions
19
The Analytic Class Number Formula
Problem set 8 due
20
The Kronecker-Weber Theorem
21
Class Field Theory: Ray Class Groups and Ray Class Fields
Problem set 9 due
22
The Main Theorems of Global Class Field Theory
23
Tate Cohomology
24
Artin Reciprocity in the Unramified Case
25
The Ring of Adeles and Strong Approximation
Problem set 10 due
26
The Idele Group, Profinite Groups, and Infinite Galois Theory
27
Local Class Field Theory
28
Global Class Field Theory and the Chebotarev Density Theorem
Problem set 11 due
