The Local Structure Of Algebraic K Theory
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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.
The Local Structure Of Algebraic K Theory
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Author : Bjorn Ian Dundas
language : en
Publisher:
Release Date : 2012-09-06
The Local Structure Of Algebraic K Theory written by Bjorn Ian Dundas and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-06 with categories.
Algebraic K Theory
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 1991
Algebraic K Theory written by 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 1991 with K-theory categories.
Algebraic K Theory And Algebraic Topology
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Author : P.G. Goerss
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Algebraic K Theory And Algebraic Topology written by P.G. Goerss 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 2013-04-17 with Mathematics categories.
A NATO Advanced Study Institute entitled "Algebraic K-theory and Algebraic Topology" was held at Chateau Lake Louise, Lake Louise, Alberta, Canada from December 12 to December 16 of 1991. This book is the volume of proceedings for this meeting. The papers that appear here are representative of most of the lectures that were given at the conference, and therefore present a "snapshot" of the state ofthe K-theoretic art at the end of 1991. The underlying objective of the meeting was to discuss recent work related to the Lichtenbaum-Quillen complex of conjectures, fro~ both the algebraic and topological points of view. The papers in this volume deal with a range of topics, including motivic cohomology theories, cyclic homology, intersection homology, higher class field theory, and the former telescope conjecture. This meeting was jointly funded by grants from NATO and the National Science Foun dation in the United States. I would like to take this opportunity to thank these agencies for their support. I would also like to thank the other members of the organizing com mittee, namely Paul Goerss, Bruno Kahn and Chuck Weibel, for their help in making the conference successful. This was the second NATO Advanced Study Institute to be held in this venue; the first was in 1987. The success of both conferences owes much to the professionalism and helpfulness of the administration and staff of Chateau Lake Louise.
Algebraic K Theory
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Author : Vasudevan Srinivas
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21
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 2013-11-21 with Science categories.
Algebraic K Theory
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Author : Richard G. Swan
language : en
Publisher: Springer
Release Date : 2006-11-14
Algebraic K Theory written by Richard G. Swan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
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."
Introduction To Algebraic K Theory
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Author : John R. Silvester
language : en
Publisher: Chapman & Hall
Release Date : 1981
Introduction To Algebraic K Theory written by John R. Silvester and has been published by Chapman & Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
Introduction To Algebraic K Theory
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Author : John Willard Milnor
language : en
Publisher: Princeton University Press
Release Date : 1971
Introduction To Algebraic K Theory written by John Willard Milnor and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.
Algebraic K-theory describes a branch of algebra that centers about two functors. K0 and K1, which assign to each associative ring ∧ an abelian group K0∧ or K1∧ respectively. Professor Milnor sets out, in the present work, to define and study an analogous functor K2, also from associative rings to abelian groups. Just as functors K0 and K1 are important to geometric topologists, K2 is now considered to have similar topological applications. The exposition includes, besides K-theory, a considerable amount of related arithmetic.
Higher Algebraic K Theory An Overview
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Author : Emilio Lluis-Puebla
language : en
Publisher: Springer
Release Date : 2006-11-14
Higher Algebraic K Theory An Overview written by Emilio Lluis-Puebla and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
This book is a general introduction to Higher Algebraic K-groups of rings and algebraic varieties, which were first defined by Quillen at the beginning of the 70's. These K-groups happen to be useful in many different fields, including topology, algebraic geometry, algebra and number theory. The goal of this volume is to provide graduate students, teachers and researchers with basic definitions, concepts and results, and to give a sampling of current directions of research. Written by five specialists of different parts of the subject, each set of lectures reflects the particular perspective ofits author. As such, this volume can serve as a primer (if not as a technical basic textbook) for mathematicians from many different fields of interest.
Algebraic K Theory
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Author : Victor Percy Snaith
language : en
Publisher: American Mathematical Soc.
Release Date : 1997-01-01
Algebraic K Theory written by Victor Percy Snaith 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 1997-01-01 with Mathematics categories.
The conference proceedings volume is produced in connection with the second Great Lakes K-theory Conference that was held at The Fields Institute for Research in Mathematical Sciences in March 1996. The volume is dedicated to the late Bob Thomason, one of the leading research mathematicians specializing in algebraic K-theory. In addition to research papers treated directly in the lectures at the conference, this volume contains the following: i) several timely articles inspired by those lectures (particularly by that of V. Voevodsky), ii) an extensive exposition by Steve Mitchell of Thomason's famous result concerning the relationship between algebraic K-theory and etale cohomology, iii) a definitive exposition by J-L. Colliot-Thelene, R. Hoobler, and B. Kahn (explaining and elaborating upon unpublished work of O. Gabber) of Bloch-Ogus-Gersten type resolutions in K-theory and algebraic geometry. This volume will be important both for researchers who want access to details of recent development in K-theory and also to graduate students and researchers seeking good advanced exposition.