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Author | : Jonathan Rosenberg |
Publisher | : Springer Science & Business Media |
Total Pages | : 404 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461243149 |
Download Algebraic K-Theory and Its Applications Book in PDF, ePub and Kindle
Algebraic K-Theory is crucial in many areas of modern mathematics, especially algebraic topology, number theory, algebraic geometry, and operator theory. This text is designed to help graduate students in other areas learn the basics of K-Theory and get a feel for its many applications. Topics include algebraic topology, homological algebra, algebraic number theory, and an introduction to cyclic homology and its interrelationship with K-Theory.
Author | : Jonathan Rosenberg |
Publisher | : Springer Science & Business Media |
Total Pages | : 408 |
Release | : 1995-12-22 |
Genre | : Mathematics |
ISBN | : 0387942483 |
Download Algebraic K-Theory and Its Applications Book in PDF, ePub and Kindle
Algebraic K-Theory is crucial in many areas of modern mathematics, especially algebraic topology, number theory, algebraic geometry, and operator theory. This text is designed to help graduate students in other areas learn the basics of K-Theory and get a feel for its many applications. Topics include algebraic topology, homological algebra, algebraic number theory, and an introduction to cyclic homology and its interrelationship with K-Theory.
Author | : Hvedri Inassaridze |
Publisher | : Springer Science & Business Media |
Total Pages | : 444 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 9401585695 |
Download Algebraic K-Theory Book in PDF, ePub and Kindle
Algebraic K-theory is a modern branch of algebra which has many important applications in fundamental areas of mathematics connected with algebra, topology, algebraic geometry, functional analysis and algebraic number theory. Methods of algebraic K-theory are actively used in algebra and related fields, achieving interesting results. This book presents the elements of algebraic K-theory, based essentially on the fundamental works of Milnor, Swan, Bass, Quillen, Karoubi, Gersten, Loday and Waldhausen. It includes all principal algebraic K-theories, connections with topological K-theory and cyclic homology, applications to the theory of monoid and polynomial algebras and in the theory of normed algebras. This volume will be of interest to graduate students and research mathematicians who want to learn more about K-theory.
Author | : Hyman Bass |
Publisher | : World Scientific |
Total Pages | : 622 |
Release | : 1999-03-12 |
Genre | : |
ISBN | : 9814544795 |
Download Algebraic K-theory And Its Applications - Proceedings Of The School Book in PDF, ePub and Kindle
The Proceedings volume is divided into two parts. The first part consists of lectures given during the first two weeks devoted to a workshop featuring state-of-the-art expositions on 'Overview of Algebraic K-theory' including various constructions, examples, and illustrations from algebra, number theory, algebraic topology, and algebraic/differential geometry; as well as on more concentrated topics involving connections of K-theory with Galois, etale, cyclic, and motivic (co)homologies; values of zeta functions, and Arithmetics of Chow groups and zero cycles. The second part consists of research papers arising from the symposium lectures in the third week.
Author | : Bjørn Ian Dundas |
Publisher | : Springer Science & Business Media |
Total Pages | : 447 |
Release | : 2012-09-06 |
Genre | : Mathematics |
ISBN | : 1447143930 |
Download The Local Structure of Algebraic K-Theory Book in PDF, ePub and Kindle
Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homological invariants offered by motivic cohomology and topological cyclic homology. This book covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference between the theories are ‘locally constant’. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain a host of ‘nearby’ calculations in K-theory. For instance, Quillen's calculation of the K-theory of finite fields gives rise to Hesselholt and Madsen's calculations for local fields, and Voevodsky's calculations for the integers give insight into the diffeomorphisms of manifolds. In addition to the proof of the full integral version of the local correspondence between K-theory and topological cyclic homology, the book provides an introduction to the necessary background in algebraic K-theory and highly structured homotopy theory; collecting all necessary tools into one common framework. It relies on simplicial techniques, and contains an appendix summarizing the methods widely used in the field. The book is intended for graduate students and scientists interested in algebraic K-theory, and presupposes a basic knowledge of algebraic topology.
Author | : Charles A. Weibel |
Publisher | : American Mathematical Soc. |
Total Pages | : 634 |
Release | : 2013-06-13 |
Genre | : Mathematics |
ISBN | : 0821891324 |
Download The $K$-book Book in PDF, ePub and Kindle
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 algebr
Author | : Bruce A. Magurn |
Publisher | : Cambridge University Press |
Total Pages | : 704 |
Release | : 2002-05-20 |
Genre | : Mathematics |
ISBN | : 1107079446 |
Download An Algebraic Introduction to K-Theory Book in PDF, ePub and Kindle
This is an introduction to algebraic K-theory with no prerequisite beyond a first semester of algebra (including Galois theory and modules over a principal ideal domain). The presentation is almost entirely self-contained, and is divided into short sections with exercises to reinforce the ideas and suggest further lines of inquiry. No experience with analysis, geometry, number theory or topology is assumed. Within the context of linear algebra, K-theory organises and clarifies the relations among ideal class groups, group representations, quadratic forms, dimensions of a ring, determinants, quadratic reciprocity and Brauer groups of fields. By including introductions to standard algebra topics (tensor products, localisation, Jacobson radical, chain conditions, Dedekind domains, semi-simple rings, exterior algebras), the author makes algebraic K-theory accessible to first-year graduate students and other mathematically sophisticated readers. Even if your algebra is rusty, you can read this book; the necessary background is here, with proofs.
Author | : Richard G. Swan |
Publisher | : Springer |
Total Pages | : 269 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540359176 |
Download Algebraic K-Theory Book in PDF, ePub and Kindle
From the Introduction: "These notes are taken from a course on algebraic K-theory [given] at the University of Chicago in 1967. They also include some material from an earlier course on abelian categories, elaborating certain parts of Gabriel's thesis. The results on K-theory are mostly of a very general nature."
Author | : Vasudevan Srinivas |
Publisher | : Springer Science & Business Media |
Total Pages | : 328 |
Release | : 2013-11-21 |
Genre | : Science |
ISBN | : 1489967354 |
Download Algebraic K-Theory Book in PDF, ePub and Kindle
Author | : Vasudevan Srinivas |
Publisher | : Springer Science & Business Media |
Total Pages | : 357 |
Release | : 2009-05-21 |
Genre | : Mathematics |
ISBN | : 0817647392 |
Download Algebraic K-Theory Book in PDF, ePub and Kindle
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 students in mathematics. This book is based on lectures given by the author at the Tata Institute in Bombay and elsewhere. This new edition includes an appendix on algebraic geometry that contains required definitions and results needed to understand the core of the book.