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