http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
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.
Preface to the First Edition -- Preface to the Second Edition -- "Classical" K-Theory -- The Plus Construction -- The Classifying Space of a Small Category -- Exact Categories and Quillen's Q-Construction -- The K-Theory of Rings and Schemes -- Proofs of the Theorems of Chapter 4 -- Comparison of the Plus and Q-Constructions -- The Merkurjev--Suslin Theorem -- Localization for Singular Varieties -- Appendix A. Results from Topology -- Appendix B. Results from Category Theory -- Appendix C. Exact Couples -- Appendix D. Results from Algebraic Geometry -- Bibliography.