The Local Structure of Algebraic K-Theory (Algebra and Applications)

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9781447143925: The Local Structure of Algebraic K-Theory (Algebra and Applications)

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.

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“The comparison of K-theory with topological cyclic homology is by means of a natural transformation called the cyclotomic trace which is the principal subject of this book. ... Many references invite to further reading. The book can be highly recommended to anybody interested in the modern understanding of algebraic K-theory and its approximations by functors which are more accessible to calculations.” (Rainer Vogt, zbMATH, Vol. 1272, 2013)

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Bjorn Ian Dundas, Randy McCarthy, Thomas G. Goodwillie
Editorial: Springer London Ltd, United Kingdom (2012)
ISBN 10: 1447143922 ISBN 13: 9781447143925
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Descripción Springer London Ltd, United Kingdom, 2012. Hardback. Estado de conservación: New. 2012 ed.. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. 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 Bokstedt, 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. Nº de ref. de la librería LIE9781447143925

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Descripción Springer London Ltd, 2012. HRD. Estado de conservación: New. New Book.Shipped from US within 10 to 14 business days.THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Nº de ref. de la librería IP-9781447143925

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Descripción Springer, 2012. Hardback. Estado de conservación: NEW. 9781447143925 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Nº de ref. de la librería HTANDREE0299465

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Descripción Springer, 2016. Paperback. Estado de conservación: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Nº de ref. de la librería ria9781447143925_lsuk

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Descripción Springer London Ltd, 2012. HRD. Estado de conservación: New. New Book. Delivered from our US warehouse in 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND.Established seller since 2000. Nº de ref. de la librería IP-9781447143925

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Descripción Springer, 2012. Estado de conservación: New. This item is printed on demand for shipment within 3 working days. Nº de ref. de la librería LP9781447143925

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Descripción Springer, 2017. Hardcover. Estado de conservación: New. Never used! This item is printed on demand. Nº de ref. de la librería 1447143922

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Descripción Springer London Ltd, United Kingdom, 2012. Hardback. Estado de conservación: New. 2012 ed.. Language: English . Brand New Book ***** Print on Demand *****.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 Bokstedt, 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. Nº de ref. de la librería APC9781447143925

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Descripción Springer London Ltd. Hardcover. Estado de conservación: New. Hardcover. 435 pages. Dimensions: 9.5in. x 6.4in. x 1.2in.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 Quillens calculations of finite fields and Suslins 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 Bkstedt, Hsiang and Madsens 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, Quillens calculation of the K-theory of finite fields gives rise to Hesselholt and Madsens calculations for local fields, and Voevodskys 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. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Hardcover. Nº de ref. de la librería 9781447143925

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Descripción 2012. Hardcover. Estado de conservación: New. 12201st. Hardcover. Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic g.Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. 436 pages. 0.748. Nº de ref. de la librería 9781447143925

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