Algebraic K-theory

Based on notes from lectures given by the author at the Tata Institute in Bombay, this revised edition provides an introduction to higher K-theory. It presumes a limited background in topology and focuses on applications in algebra and algebraic geometry.

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Algebraic K-Theory is an active area of research that has connections with algebra, algebraic geometry, topology, an number theory. Based on notes from lectures given by the author at the Tata Institute in Bombay , this revised edition provides an introduction to higher K-theory for professional mathematicians and graduate students. It presumes a limited background in topology and thus provides the necessary proofs of topological results, and focuses on applications in algebra and algebraic geometry. A major part of the book is devoted to a detailed exposition of the ideas of Quillen as contained in the now classic papers 'Higher Algebraic K-theory, I, II." Beyond this, two applications are given: to the theorem of Mercurjev and Suslin relating K2 and the Brauer group of a field (given in this Second Edition in a simplified version); and to modules of finite length and recited 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.
Appendices on topological results, results from algebraic geometry, category theory and exact couples are included, to make the exposition more self-contained.