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Algebraic K Theory Number Theory Geometry And Analysis
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Book Synopsis The Local Structure of Algebraic K-Theory by : Bjørn Ian Dundas
Download or read book The Local Structure of Algebraic K-Theory written by Bjørn Ian Dundas and published by Springer Science & Business Media. This book was released on 2012-09-06 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Algebraic K-theory, Number Theory, Geometry, and Analysis by : Anthony Bak
Download or read book Algebraic K-theory, Number Theory, Geometry, and Analysis written by Anthony Bak and published by Springer. This book was released on 1984 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algebraic K-Theory by : Hvedri Inassaridze
Download or read book Algebraic K-Theory written by Hvedri Inassaridze and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Algebraic K-Theory and Its Applications by : Jonathan Rosenberg
Download or read book Algebraic K-Theory and Its Applications written by Jonathan Rosenberg and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Algebraic K-Theory by : Vasudevan Srinivas
Download or read book Algebraic K-Theory written by Vasudevan Srinivas and published by Springer Science & Business Media. This book was released on 2009-05-21 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Higher Algebraic K-Theory: An Overview by : Emilio Lluis-Puebla
Download or read book Higher Algebraic K-Theory: An Overview written by Emilio Lluis-Puebla and published by Springer. This book was released on 2006-11-14 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The $K$-book written by Charles A. Weibel and published by American Mathematical Soc.. This book was released on 2013-06-13 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Algebraic K-Theory: Connections with Geometry and Topology by : John F. Jardine
Download or read book Algebraic K-Theory: Connections with Geometry and Topology written by John F. Jardine and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Algebraic $K$-Theory by : Wayne Raskind
Download or read book Algebraic $K$-Theory written by Wayne Raskind and published by American Mathematical Soc.. This book was released on 1999 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of the Joint Summer Research Conference on Algebraic K-theory held at the University of Washington in Seattle. High-quality surveys are written by leading experts in the field. Included is an up-to-date account of Voevodsky's proof of the Milnor conjecture relating the Milnor K-theory of fields to Galois cohomology. The book is intended for graduate students and research mathematicians interested in $K$-theory, algebraic geometry, and number theory.
Book Synopsis An Algebraic Introduction to K-Theory by : Bruce A. Magurn
Download or read book An Algebraic Introduction to K-Theory written by Bruce A. Magurn and published by Cambridge University Press. This book was released on 2002-05-20 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to algebraic K-theory with no prerequisite beyond a first semester of algebra.
Book Synopsis Algebraic K-theory and Algebraic Number Theory by : Michael R. Stein
Download or read book Algebraic K-theory and Algebraic Number Theory written by Michael R. Stein and published by American Mathematical Soc.. This book was released on 1989 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Transformation Groups and Algebraic K-Theory by : Wolfgang Lück
Download or read book Transformation Groups and Algebraic K-Theory written by Wolfgang Lück and published by Springer. This book was released on 2006-11-14 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses on the relation between transformation groups and algebraic K-theory. The general pattern is to assign to a geometric problem an invariant in an algebraic K-group which determines the problem. The algebraic K-theory of modules over a category is studied extensively and appplied to the fundamental category of G-space. Basic details of the theory of transformation groups sometimes hard to find in the literature, are collected here (Chapter I) for the benefit of graduate students. Chapters II and III contain advanced new material of interest to researchers working in transformation groups, algebraic K-theory or related fields.
Book Synopsis Introduction to Algebraic K-theory by : John Willard Milnor
Download or read book Introduction to Algebraic K-theory written by John Willard Milnor and published by Princeton University Press. This book was released on 1971 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Algebraic $K$-Theory, Commutative Algebra, and Algebraic Geometry by : R. Keith Dennis
Download or read book Algebraic $K$-Theory, Commutative Algebra, and Algebraic Geometry written by R. Keith Dennis and published by American Mathematical Soc.. This book was released on 1992 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the mid-1960's, 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 US. 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 US-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.
Book Synopsis Representation Theory and Higher Algebraic K-Theory by : Aderemi Kuku
Download or read book Representation Theory and Higher Algebraic K-Theory written by Aderemi Kuku and published by CRC Press. This book was released on 2016-04-19 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Representation Theory and Higher Algebraic K-Theory is the first book to present higher algebraic K-theory of orders and group rings as well as characterize higher algebraic K-theory as Mackey functors that lead to equivariant higher algebraic K-theory and their relative generalizations. Thus, this book makes computations of higher K-theory of grou
Book Synopsis Handbook of K-Theory by : Eric Friedlander
Download or read book Handbook of K-Theory written by Eric Friedlander and published by Springer Science & Business Media. This book was released on 2005-07-18 with total page 1148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. It offers an exposition of our current state of knowledge as well as an implicit blueprint for future research.
Book Synopsis Algebraic K-Theory and Algebraic Topology by : P.G. Goerss
Download or read book Algebraic K-Theory and Algebraic Topology written by P.G. Goerss and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
