Number Theory I

Calendar

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