Algebraic K-Theory. Evanston 1980

Algebraic K-Theory. Evanston 1980
Title Algebraic K-Theory. Evanston 1980 PDF eBook
Author Eric Friedlander
Publisher Springer
Pages 526
Release 2006-11-15
Genre Mathematics
ISBN 3540386467

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Algebraic K-Theory. Proceedings of a Conference Held at Oberwolfach, June 1980

Algebraic K-Theory. Proceedings of a Conference Held at Oberwolfach, June 1980
Title Algebraic K-Theory. Proceedings of a Conference Held at Oberwolfach, June 1980 PDF eBook
Author R. Keith Dennis
Publisher Springer
Pages 419
Release 2006-11-15
Genre Mathematics
ISBN 3540395539

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Algebraic K-Theory

Algebraic K-Theory
Title Algebraic K-Theory PDF eBook
Author Hvedri Inassaridze
Publisher Springer Science & Business Media
Pages 444
Release 2013-03-14
Genre Mathematics
ISBN 9401585695

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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

Algebraic K — Theory
Title Algebraic K — Theory PDF eBook
Author R. Keith Dennis
Publisher Springer
Pages 421
Release 2006-11-15
Genre Mathematics
ISBN 3540395563

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Algebraic K-theory and Algebraic Number Theory

Algebraic K-theory and Algebraic Number Theory
Title Algebraic K-theory and Algebraic Number Theory PDF eBook
Author Michael R. Stein
Publisher American Mathematical Soc.
Pages 506
Release 1989
Genre Mathematics
ISBN 0821850903

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This volume contains the proceedings of a seminar on Algebraic $K$-theory and Algebraic Number Theory, held at the East-West Center in Honolulu in January 1987. The seminar, which hosted nearly 40 experts from the U.S. and Japan, was motivated by the wide range of connections between the two topics, as exemplified in the work of Merkurjev, Suslin, Beilinson, Bloch, Ramakrishnan, Kato, Saito, Lichtenbaum, Thomason, and Ihara. As is evident from the diversity of topics represented in these proceedings, the seminar provided an opportunity for mathematicians from both areas to initiate further interactions between these two areas.

Algebraic K-theory And Its Applications - Proceedings Of The School

Algebraic K-theory And Its Applications - Proceedings Of The School
Title Algebraic K-theory And Its Applications - Proceedings Of The School PDF eBook
Author Hyman Bass
Publisher World Scientific
Pages 622
Release 1999-03-12
Genre
ISBN 9814544795

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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.

The Local Structure of Algebraic K-Theory

The Local Structure of Algebraic K-Theory
Title The Local Structure of Algebraic K-Theory PDF eBook
Author Bjørn Ian Dundas
Publisher Springer Science & Business Media
Pages 447
Release 2012-09-06
Genre Mathematics
ISBN 1447143930

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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.