Algebraic Number Theory - J.S. Milne Top

Group Theory

Fields and Galois Theory

Algebraic Geometry

Algebraic Number Theory

Modular Functions and Modular Forms

Elliptic Curves -- see books.

Abelian Varieties

Lectures on Etale Cohomology

Class Field Theory

Complex Multiplication

Basic Theory of Affine Group Schemes

Lie Algebras, Algebraic Groups, and Lie Groups

Reductive Groups

Errata

pdf file for printing (11pt; a4paper; margins)

Same file with margins cropped --- may be better for viewing on gadgets.

pdf file formatted for ereaders (9pt; 89mm x 120mm; 5mm margins)(3.03)

This is a fairly standard graduate course on algebraic number theory.

- Preliminaries From Commutative Algebra
- Rings of Integers
- Dedekind Domains; Factorization
- The Finiteness of the Class Number
- The Unit Theorem
- Cyclotomic Extensions; Fermat's Last Theorem
- Valuations; Local Fields
- Global Fields

v2.10; August 31, 1998; fixed many minor errors; added exercises and index; 140p.

v3.00; February 11, 2008; corrected; revisions and additions; 163 pages.

v3.01; September 28, 2008; fixed a problem with the hyperlinks; 163 pages.

v3.02; April 30, 2009; fixed many minor errors; changed chapter and pages styles; 164 pages.

v3.03; May 29, 2011; minor fixes; 167 pages.

v3.04; April 16, 2012; minor fixes; 160 pages.

v3.05; March, 21, 2013; minor fixes; 161 pages.

v3.06; May, 28, 2014; minor fixes; added Hermite's theorem; 164 pages.

v3.07; March 18, 2017; minor fixes; 165 pages.

pdf (old version 2.10)

pdf (old version 3.00)

pdf (old version 3.01)