Algebraic K Theory And Its Geometric Applications
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Algebraic K Theory And Its Geometric Applications
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Author : Robert M.F. Moss
language : en
Publisher: Springer
Release Date : 2006-11-15
Algebraic K Theory And Its Geometric Applications written by Robert M.F. Moss and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Algebraic K Theory And Its Applications
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Author : Jonathan Rosenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebraic K Theory And Its Applications written by Jonathan Rosenberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Algebraic K Theory
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Author : Hvedri Inassaridze
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Algebraic K Theory written by Hvedri Inassaridze and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
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.
Algebraic K Theory Iii Proceedings Of The Conference Held At The Seattle Research Center Of Battelle Memorial Institute August 28 September 8 1972
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Author : Hyman Bass
language : en
Publisher: Springer
Release Date : 2006-11-15
Algebraic K Theory Iii Proceedings Of The Conference Held At The Seattle Research Center Of Battelle Memorial Institute August 28 September 8 1972 written by Hyman Bass and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
The Local Structure Of Algebraic K Theory
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Author : Bjørn Ian Dundas
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-06
The Local Structure Of Algebraic K Theory written by Bjørn Ian Dundas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-06 with Mathematics categories.
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.
Algebraic K Theory
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Author : Vasudevan Srinivas
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-21
Algebraic K Theory written by Vasudevan Srinivas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-21 with Mathematics categories.
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.
Hermitian K Theory And Geometric Applications
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Author :
language : en
Publisher:
Release Date : 1973
Hermitian K Theory And Geometric Applications written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with categories.
Algebraic K Theory Connections With Geometry And Topology
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Author : John F. Jardine
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebraic K Theory Connections With Geometry And Topology written by John F. Jardine and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A NATO Advanced Study Institute entitled "Algebraic K-theory: Connections with Geometry and Topology" was held at the Chateau Lake Louise, Lake Louise, Alberta, Canada from December 7 to December 11 of 1987. This meeting was jointly supported by NATO and the Natural Sciences and Engineering Research Council of Canada, and was sponsored in part by the Canadian Mathematical Society. This book is the volume of proceedings for that meeting. Algebraic K-theory is essentially the study of homotopy invariants arising from rings and their associated matrix groups. More importantly perhaps, the subject has become central to the study of the relationship between Topology, Algebraic Geometry and Number Theory. It draws on all of these fields as a subject in its own right, but it serves as well as an effective translator for the application of concepts from one field in another. The papers in this volume are representative of the current state of the subject. They are, for the most part, research papers which are primarily of interest to researchers in the field and to those aspiring to be such. There is a section on problems in this volume which should be of particular interest to students; it contains a discussion of the problems from Gersten's well-known list of 1973, as well as a short list of new problems.
Algebraic K Theory Hermitian K Theory And Geometric Applications
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Author : Hyman Bass
language : en
Publisher:
Release Date : 1973
Algebraic K Theory Hermitian K Theory And Geometric Applications written by Hyman Bass and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Associative rings categories.
Algebraic K Theory Commutative Algebra And Algebraic Geometry
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Author : R. Keith Dennis
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Algebraic K Theory Commutative Algebra And Algebraic Geometry written by R. Keith Dennis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
In the mid-1960s, several Italian mathematicians began to study the connections between classical arguments in commutative algebra and algebraic geometry, and the contemporaneous development of algebraic $K$-theory in the U.S. These connections were exemplified by the work of Andreotti-Bombieri, Salmon, and Traverso on seminormality, and by Bass-Murthy on the Picard groups of polynomial rings. Interactions proceeded far beyond this initial point to encompass Chow groups of singular varieties, complete intersections, and applications of $K$-theory to arithmetic and real geometry. This volume contains the proceedings from a U.S.-Italy Joint Summer Seminar, which focused on this circle of ideas. The conference, held in June 1989 in Santa Margherita Ligure, Italy, was supported jointly by the Consiglio Nazionale delle Ricerche and the National Science Foundation. The book contains contributions from some of the leading experts in this area.