Author | Srinivas, V. author |
---|---|

Title | Algebraic K-Theory [electronic resource] / by V. Srinivas |

Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1996 |

Edition | Second Edition |

Connect to | http://dx.doi.org/10.1007/978-0-8176-4739-1 |

Descript | XVII, 341 p. online resource |

SUMMARY

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

CONTENT

โ{128}{156}Classicalโ{128}{157} K-Theory -- The Plus Construction -- The Classifying Space of a Small Category -- Exact Categories and Quillenโ{128}{153}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

Mathematics
Algebraic geometry
K-theory
Topology
Algebraic topology
Mathematics
K-Theory
Algebraic Geometry
Algebraic Topology
Topology