Srinivas Algebraic K-Theory

2. Auflage 1996
ISBN: 978-0-8176-4739-1
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 341 Seiten, eBook

Reihe: Modern Birkhäuser Classics

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. This new 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 applications 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.

Zielgruppe

Research

Autoren/Hrsg.

Srinivas, Vasudevan

Inhaltsverzeichnis

“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.