Download or read book Algebraic K Theory written by Vasudevan Srinivas and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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
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.
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.
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.
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 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.
Download or read book Algebraic Geometry written by Robin Hartshorne and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.
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.
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.
Download or read book Algebraic K theory written by Victor Percy Snaith and published by American Mathematical Soc.. This book was released on 1997-01-01 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Download or read book K Theory written by Max Karoubi and published by Springer Science & Business Media. This book was released on 2009-11-27 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Preface: K-theory was introduced by A. Grothendieck in his formulation of the Riemann- Roch theorem. For each projective algebraic variety, Grothendieck constructed a group from the category of coherent algebraic sheaves, and showed that it had many nice properties. Atiyah and Hirzebruch considered a topological analog defined for any compact space X, a group K{X) constructed from the category of vector bundles on X. It is this ''topological K-theory" that this book will study. Topological K-theory has become an important tool in topology. Using K- theory, Adams and Atiyah were able to give a simple proof that the only spheres which can be provided with H-space structures are S1, S3 and S7. Moreover, it is possible to derive a substantial part of stable homotopy theory from K-theory. The purpose of this book is to provide advanced students and mathematicians in other fields with the fundamental material in this subject. In addition, several applications of the type described above are included. In general we have tried to make this book self-contained, beginning with elementary concepts wherever possible; however, we assume that the reader is familiar with the basic definitions of homotopy theory: homotopy classes of maps and homotopy groups.Thus this book might be regarded as a fairly self-contained introduction to a "generalized cohomology theory".
Download or read book Algebraic K Theory written by Richard G. Swan and published by Springer. This book was released on 2006-11-14 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."
Download or read book Motivic Homotopy Theory written by Bjorn Ian Dundas and published by Springer Science & Business Media. This book was released on 2007-07-11 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Aimed at graduate students in algebraic topology and algebraic geometry, it contains background material from both of these fields, as well as the foundations of motivic homotopy theory. It will serve as a good introduction as well as a convenient reference for a broad group of mathematicians to this important and fascinating new subject. Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work, and the other authors have all done important work in the subject.
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.
Download or read book Mixed Motives and Algebraic K Theory written by Uwe Jannsen and published by Springer. This book was released on 2006-11-14 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: The relations that could or should exist between algebraic cycles, algebraic K-theory, and the cohomology of - possibly singular - varieties, are the topic of investigation of this book. The author proceeds in an axiomatic way, combining the concepts of twisted Poincaré duality theories, weights, and tensor categories. One thus arrives at generalizations to arbitrary varieties of the Hodge and Tate conjectures to explicit conjectures on l-adic Chern characters for global fields and to certain counterexamples for more general fields. It is to be hoped that these relations ions will in due course be explained by a suitable tensor category of mixed motives. An approximation to this is constructed in the setting of absolute Hodge cycles, by extending this theory to arbitrary varieties. The book can serve both as a guide for the researcher, and as an introduction to these ideas for the non-expert, provided (s)he knows or is willing to learn about K-theory and the standard cohomology theories of algebraic varieties.
