The Kbook : an introduction to algebraic Ktheory
 Responsibility
 Charles A. Weibel.
 Language
 English.
 Publication
 Providence, Rhode Island : American Mathematical Society, [2013]
 Physical description
 xii, 618 pages : illustrations ; 25 cm.
 Series
 Graduate studies in mathematics ; v. 145.
Access
Available online
Math & Statistics Library
Stacks
Call number  Status 

QA612.33 .W45 2013  Unknown 
More options
Creators/Contributors
 Author/Creator
 Weibel, Charles A., 1950
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 589598) and indexes.
 Contents

 Projective modules and vector bundles The Grothendieck group $K_0$ $K_1$ and $K_2$ of a ring Definitions of higher $K$theory The fundamental theorems of higher $K$theory The higher $K$theory of fields Nomenclature Bibliography Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 Informally, $K$theory is a tool for probing the structure of a mathematical object such as a ring or a topological space in terms of suitably parameterized vector spaces and producing important intrinsic invariants which are useful in the study of algebraic and geometric questions. Algebraic $K$theory, which is the main character of this book, deals mainly with studying the structure of rings. However, it turns out that even working in a purely algebraic context, one requires techniques from homotopy theory to construct the higher $K$groups and to perform computations. The resulting interplay of algebra, geometry, and topology in $K$theory provides a fascinating glimpse of the unity of mathematics. This book is a comprehensive introduction to the subject of algebraic $K$theory. It blends classical algebraic techniques for $K_0$ and $K_1$ with newer topological techniques for higher $K$theory such as homotopy theory, spectra, and cohomological descent. The book takes the reader from the basics of the subject to the state of the art, including the calculation of the higher $K$theory of number fields and the relation to the Riemann zeta function.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2013
 Series
 Graduate studies in mathematics ; v. 145
 ISBN
 9780821891322 (alk. paper)
 0821891324 (alk. paper)