Algebraic K-Theory

  • V. Srinivas

Part of the Modern Birkhauser Classics book series (MBC)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. V. Srinivas
    Pages 1-17
  3. V. Srinivas
    Pages 18-30
  4. V. Srinivas
    Pages 46-88
  5. V. Srinivas
    Pages 89-125
  6. V. Srinivas
    Pages 126-144
  7. V. Srinivas
    Pages 145-193
  8. V. Srinivas
    Pages 194-229
  9. Back Matter
    Pages 230-341

About this book

Introduction

Algebraic K-Theory has become an increasingly active area of research. With its connections to algebra, algebraic geometry, topology, and number theory, it has implications for a wide variety of researchers and graduate students in mathematics. The book is based on lectures given at the author's home institution, the Tata Institute in Bombay, and elsewhere. A detailed appendix on topology was provided in the first edition to make the treatment accessible to readers with a limited background in topology. The second edition also includes an appendix on algebraic geometry that contains the required definitions and results needed to understand the core of the book; this makes the book accessible to a wider audience.

A central part of the book is a detailed exposition of the ideas of Quillen as contained in his classic papers "Higher Algebraic K-Theory, I, II." A more elementary proof of the theorem of Merkujev--Suslin is given in this edition; this makes the treatment of this topic self-contained. An application is also given to modules of finite length and finite projective dimension over the local ring of a normal surface singularity. These results lead the reader to some interesting conclusions regarding the Chow group of varieties.

 

"It is a pleasure to read this mathematically beautiful book..." ---WW.J. Julsbergen, Mathematics Abstracts

"The book does an admirable job of presenting the details of Quillen's work..." ---Mathematical Reviews

Keywords

Category theory Dimension Grad K-theory algebraic geometry plus construction topology

Authors and affiliations

  • V. Srinivas
    • 1
  1. 1.School of MathematicsTata Institute of Fundamental ResearchBombayIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4739-1
  • Copyright Information Springer Science+Business Media New York 1996
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-8176-4736-0
  • Online ISBN 978-0-8176-4739-1
  • Series Print ISSN 2197-1803
  • Series Online ISSN 2197-1811
  • Buy this book on publisher's site