Number Theory II: Class Field Theory

Lecture Notes

This is the complete Lecture Notes (PDF - 1.6MB) file with table of contents, index, and bibliography. (Complete lecture notes and the following lecture notes courtesy of Oron Propp. Used with permission.)

LEC #	TOPICS
1	Introduction (PDF)
2	Hilbert Symbols (PDF)
3	Norm Groups with Tame Ramification (PDF)
4	GCFT and Quadratic Reciprocity (PDF)
5	Non-Degeneracy of the Adèle Pairing and Exact Sequences (PDF)
6	Exact Sequences and Tate Cohomology (PDF)
7	Chain Complexes and Herbrand Quotients (PDF)
8	Tate Cohomology and Inverse Limits (PDF)
9	Hilbert’s Theorem 90 and Cochain Complexes (PDF)
10	Homotopy, Quasi-Isomorphism, and Coinvariants (PDF)
11	The Mapping Complex and Projective Resolutions (PDF)
12	Derived Functors and Explicit Projective Resolutions (PDF)
13	Homotopy Coinvariants, Abelianization, and Tate Cohomology (PDF)
14	Tate Cohomology and K{{< sup “unr” >}} (PDF)
15	The Vanishing Theorem Implies Cohomological LCFT (PDF)
16	Vanishing of Tate Cohomology Groups (PDF)
17	Proof of the Vanishing Theorem (PDF)
18	Norm Groups, Kummer Theory, and Profinite Cohomology (PDF)
19	Brauer Groups (PDF)
20	Proof of the First Inequality (PDF)
21	Artin and Brauer Reciprocity, Part I (PDF)
22	Artin and Brauer Reciprocity, Part II (PDF)
23	Proof of the Second Inequality (PDF)