Algebraic K-Theory

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, algebraic k-theory has implications for a wide variety of researchers and graduate students in mathematics. 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.

Appendices on topology and algebraic geometry provide requisite background material for the subject Provides many examples to solidify understanding in the reader Discusses fundamentals and new research extensions

Résumé
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 new edition includes an appendix on algebraic geometry that contains required definitions and results needed to understand the core of the book.

Contenu
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.