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Algebraic K-Theory (Modern Birkhauser Classics)

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Synopses & Reviews

Publisher Comments:

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

Synopsis:

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 students in mathematics. This book is based on lectures given by the author at the Tata Institute in Bombay and elsewhere. This new edition includes an appendix on algebraic geometry that contains required definitions and results needed to understand the core of the book.

Table of Contents

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.

Product Details

ISBN:
9780817647360
Author:
Srinivas, V.
Publisher:
Birkhauser
Author:
Srinivas, Vasudevan
Location:
Boston, MA
Subject:
Algebra - Linear
Subject:
Geometry - Algebraic
Subject:
Topology - General
Subject:
Algebra - General
Subject:
Category theory
Subject:
K-theory
Subject:
plus construction
Subject:
Algebraic Geometry
Subject:
Algebraic topology
Subject:
Topology
Subject:
Topology <P>The book is based on lectures given at the author s home institution, the Tata Institute in Bombay, and elsewhere. With its connections to algebra, algebraic geometry, topology, and number theory,&nbsp;algebraic k-theory&nbsp;has implications
Subject:
Mathematics-Linear Algebra
Subject:
Algebra - Abstract
Subject:
Mathematics
Subject:
B
Subject:
mathematics and statistics
Copyright:
Edition Description:
Reprint of the 1995 2nd ed.
Series:
Modern Birkhäuser Classics
Publication Date:
20071113
Binding:
TRADE PAPER
Language:
English
Pages:
358
Dimensions:
235 x 155 mm

Related Subjects

Science and Mathematics » Mathematics » Algebra » Linear Algebra
Science and Mathematics » Mathematics » Differential Geometry
Science and Mathematics » Mathematics » Geometry » Algebraic Geometry
Science and Mathematics » Mathematics » Group Theory
Science and Mathematics » Mathematics » Topology

Algebraic K-Theory (Modern Birkhauser Classics) New Trade Paper
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Product details 358 pages Birkhauser Boston - English 9780817647360 Reviews:
"Synopsis" by , 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 students in mathematics. This book is based on lectures given by the author at the Tata Institute in Bombay and elsewhere. This new edition includes an appendix on algebraic geometry that contains required definitions and results needed to understand the core of the book.
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