Synopses & Reviews
This book provides a fairly elementary and self-contained introduction to local fields.
Synopsis
Provides a self-contained introduction at the post-graduate level in number theory or algebra. After a general introduction the book focuses on p-adic numbers and their use in the theory of numbers. There are also chapters on algebraic number theory, on diophantine equations and on the analysis of a p-adic variable.
Table of Contents
Preface; Leitfaden; Notational conventions; 1. Introduction; 2. General properties; 3. Archimedean valuations; 4. Non archimedean valuations; 5. Embedding theorem; 6. Transcendental extensions; 7. Algebraic extensions; 8. p-adic fields; 9. Algebraic extensions; 10. Algebraic number fields; 11. Diophantine equations; 12. Advanced analysis; 13. A theorem of Borel and work; Appendices; References; Index.