Class Field Theory - J.S. Milne   Top
pdf file for the current version (4.03)
Same file with margins cropped.

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.

Contents

  1. Local Class Field Theory: Lubin-Tate Extensions
  2. Cohomology of Groups.
  3. Local Class Field Theory Continued.
  4. Brauer Groups
  5. Global Class Field Theory: Statements
  6. L-series and the Density of Primes
  7. Global Class Field Theory: Proofs
  8. Complements (Power reciprocity laws; quadratic forms; etc.)

Prerequisites

The algebra usually covered in first-year graduate courses and a course in algebraic number theory (for example, my online notes).

History

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.
v4.03; August 6, 2020; corrected; 296 pages.

pdf (old version 3.10)