pdf file for the current version (4.02)
This is a course on Class Field Theory, roughly along the lines of Artin and Tate and of the articles
of Serre and Tate in Cassels-Fröhlich, except that the notes are more
detailed and cover more.
- Local Class Field Theory: Lubin-Tate Extensions
- Cohomology of Groups.
- Local Class Field Theory Continued.
- Brauer Groups
- Global Class Field Theory: Statements
- L-series and the Density of Primes
- Global Class Field Theory: Proofs
- Complements (Power reciprocity laws; quadratic forms; etc.)
The algebra usually covered in first-year graduate courses and a course in
algebraic number theory (for example, my online notes).
v2.01; first version on the web.
v3.10; May 6, 1997; substantially revised and expanded from v2.01; index; 222 pages.
v4.00; March 2, 2008; corrected, revised, and expanded; 287 pages.
v4.01; May 30, 2011; corrected; 287 pages.
v4.02; March 23, 2013; corrected; 289 pages.
pdf (old version 3.10)