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Introduction to Cyclotomic Fields

  • Lawrence C. Washington

Part of the Graduate Texts in Mathematics book series (GTM, volume 83)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Lawrence C. Washington
    Pages 1-8
  3. Lawrence C. Washington
    Pages 9-18
  4. Lawrence C. Washington
    Pages 19-28
  5. Lawrence C. Washington
    Pages 29-46
  6. Lawrence C. Washington
    Pages 47-86
  7. Lawrence C. Washington
    Pages 87-112
  8. Lawrence C. Washington
    Pages 113-142
  9. Lawrence C. Washington
    Pages 143-166
  10. Lawrence C. Washington
    Pages 167-183
  11. Lawrence C. Washington
    Pages 184-203
  12. Lawrence C. Washington
    Pages 204-230
  13. Lawrence C. Washington
    Pages 231-262
  14. Lawrence C. Washington
    Pages 263-318
  15. Lawrence C. Washington
    Pages 319-330
  16. Back Matter
    Pages 331-392

About this book

Introduction

This book grew. out of lectures given at the University of Maryland in 1979/1980. The purpose was to give a treatment of p-adic L-functions and cyclotomic fields, including Iwasawa's theory of Zp-extensions, which was accessible to mathematicians of varying backgrounds. The reader is assumed to have had at least one semester of algebraic number theory (though one of my students took such a course concurrently). In particular, the following terms should be familiar: Dedekind domain, class number, discriminant, units, ramification, local field. Occasionally one needs the fact that ramification can be computed locally. However, one who has a good background in algebra should be able to survive by talking to the local algebraic number theorist. I have not assumed class field theory; the basic facts are summarized in an appendix. For most of the book, one only needs the fact that the Galois group of the maximal unramified abelian extension is isomorphic to the ideal class group, and variants of this statement. The chapters are intended to be read consecutively, but it should be possible to vary the order considerably. The first four chapters are basic. After that, the reader willing to believe occasional facts could probably read the remaining chapters randomly. For example, the reader might skip directly to Chapter 13 to learn about Zp-extensions. The last chapter, on the Kronecker-Weber theorem, can be read after Chapter 2.

Keywords

Fields Kreiskörper algebra algebraic number theory field number theory

Authors and affiliations

  • Lawrence C. Washington
    • 1
  1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-0133-2
  • Copyright Information Springer-Verlag New York 1982
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-0135-6
  • Online ISBN 978-1-4684-0133-2
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site