A COMPUTATIONAL APPROACH

**William Stein**

- Contents

- Algebraic Number Fields
- Basic Commutative Algebra
- Dedekind Domains and Unique Factorization of Ideals
- Factoring Primes
- The Chinese Remainder Theorem
- Discrimants and Norms
- Finiteness of the Class Group
- Dirichlet's Unit Theorem
- Decomposition and Inertia Groups
- Elliptic Curves, Galois Representations, and -functions
- Galois Cohomology
- The Weak Mordell-Weil Theorem

- Adelic Viewpoint
- Valuations
- Topology and Completeness
- Adic Numbers: The Finite Residue Field Case
- Normed Spaces and Tensor Products
- Extensions and Normalizations of Valuations
- Global Fields and Adeles
- Ideles and Ideals
- Exercises

- Bibliography
- About this document ...

William Stein 2012-09-24