Categories And Modules With K Theory In View
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Categories And Modules With K Theory In View
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Author : A. J. Berrick
language : en
Publisher: Cambridge University Press
Release Date : 2000-05-25
Categories And Modules With K Theory In View written by A. J. Berrick and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-05-25 with Mathematics categories.
This book, first published in 2000, develops aspects of category theory fundamental to the study of algebraic K-theory. Ring and module theory illustrates category theory which provides insight into more advanced topics in module theory. Starting with categories in general, the text then examines categories of K-theory. This leads to the study of tensor products and the Morita theory. The categorical approach to localizations and completions of modules is formulated in terms of direct and inverse limits, prompting a discussion of localization of categories in general. Finally, local-global techniques which supply information about modules from their localizations and completions and underlie some interesting applications of K-theory to number theory and geometry are considered. Many useful exercises, concrete illustrations of abstract concepts placed in their historical settings and an extensive list of references are included. This book will help all who wish to work in K-theory to master its prerequisites.
Categories And Modules With K Theory In View
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Author : A. Jon Berrick
language : en
Publisher:
Release Date : 2000
Categories And Modules With K Theory In View written by A. Jon Berrick and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Categories (Mathematics) categories.
This book, first published in 2000, develops aspects of category theory fundamental to the study of algebraic K-theory. Ring and module theory illustrates category theory which provides insight into more advanced topics in module theory. Starting with categories in general, the text then examines categories of K-theory. This leads to the study of tensor products and the Morita theory. The categorical approach to localizations and completions of modules is formulated in terms of direct and inverse limits, prompting a discussion of localization of categories in general. Finally, local-global techniques which supply information about modules from their localizations and completions and underlie some interesting applications of K-theory to number theory and geometry are considered. Many useful exercises, concrete illustrations of abstract concepts placed in their historical settings and an extensive list of references are included. This book will help all who wish to work in K-theory to master its prerequisites.
An Introduction To Rings And Modules
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Author : A. J. Berrick
language : en
Publisher: Cambridge University Press
Release Date : 2000-05-01
An Introduction To Rings And Modules written by A. J. Berrick and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-05-01 with Mathematics categories.
This concise introduction to ring theory, module theory and number theory is ideal for a first year graduate student, as well as being an excellent reference for working mathematicians in other areas. Starting from definitions, the book introduces fundamental constructions of rings and modules, as direct sums or products, and by exact sequences. It then explores the structure of modules over various types of ring: noncommutative polynomial rings, Artinian rings (both semisimple and not), and Dedekind domains. It also shows how Dedekind domains arise in number theory, and explicitly calculates some rings of integers and their class groups. About 200 exercises complement the text and introduce further topics. This book provides the background material for the authors' forthcoming companion volume Categories and Modules. Armed with these two texts, the reader will be ready for more advanced topics in K-theory, homological algebra and algebraic number theory.
An Introduction To Nonlinear Analysis
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Author : Martin Schechter
language : en
Publisher: Cambridge University Press
Release Date : 2004
An Introduction To Nonlinear Analysis written by Martin Schechter and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
The techniques that can be used to solve non-linear problems are far different than those that are used to solve linear problems. Many courses in analysis and applied mathematics attack linear cases simply because they are easier to solve and do not require a large theoretical background in order to approach them. Professor Schechter's 2005 book is devoted to non-linear methods using the least background material possible and the simplest linear techniques. An understanding of the tools for solving non-linear problems is developed whilst demonstrating their application to problems in one dimension and then leading to higher dimensions. The reader is guided using simple exposition and proof, assuming a minimal set of pre-requisites. For completion, a set of appendices covering essential basics in functional analysis and metric spaces is included, making this ideal as an accompanying text on an upper-undergraduate or graduate course, or even for self-study.
Complex Topological K Theory
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Author : Efton Park
language : en
Publisher: Cambridge University Press
Release Date : 2008-03-13
Complex Topological K Theory written by Efton Park and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-13 with Mathematics categories.
Topological K-theory is a key tool in topology, differential geometry and index theory, yet this is the first contemporary introduction for graduate students new to the subject. No background in algebraic topology is assumed; the reader need only have taken the standard first courses in real analysis, abstract algebra, and point-set topology. The book begins with a detailed discussion of vector bundles and related algebraic notions, followed by the definition of K-theory and proofs of the most important theorems in the subject, such as the Bott periodicity theorem and the Thom isomorphism theorem. The multiplicative structure of K-theory and the Adams operations are also discussed and the final chapter details the construction and computation of characteristic classes. With every important aspect of the topic covered, and exercises at the end of each chapter, this is the definitive book for a first course in topological K-theory.
Algebraic K Theory And Its Applications Proceedings Of The School
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Author : Hyman Bass
language : en
Publisher: World Scientific
Release Date : 1999-03-12
Algebraic K Theory And Its Applications Proceedings Of The School written by Hyman Bass and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-03-12 with categories.
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.
Lectures In Logic And Set Theory Volume 2 Set Theory
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Author : George Tourlakis
language : en
Publisher: Cambridge University Press
Release Date : 2003-02-13
Lectures In Logic And Set Theory Volume 2 Set Theory written by George Tourlakis and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-02-13 with Mathematics categories.
This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume II, on formal (ZFC) set theory, incorporates a self-contained 'chapter 0' on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques will provide the reader with a solid foundation in set theory and provides a context for the presentation of advanced topics such as absoluteness, relative consistency results, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and a chapter on Cohen forcing.
Completely Bounded Maps And Operator Algebras
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Author : Vern Paulsen
language : en
Publisher: Cambridge University Press
Release Date : 2002
Completely Bounded Maps And Operator Algebras written by Vern Paulsen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
In this book, first published in 2003, the reader is provided with a tour of the principal results and ideas in the theories of completely positive maps, completely bounded maps, dilation theory, operator spaces and operator algebras, together with some of their main applications. The author assumes only that the reader has a basic background in functional analysis, and the presentation is self-contained and paced appropriately for graduate students new to the subject. Experts will also want this book for their library since the author illustrates the power of methods he has developed with new and simpler proofs of some of the major results in the area, many of which have not appeared earlier in the literature. An indispensable introduction to the theory of operator spaces for all who want to know more.
Soliton Equations And Their Algebro Geometric Solutions Volume 1 1 1 Dimensional Continuous Models
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Author : Fritz Gesztesy
language : en
Publisher: Cambridge University Press
Release Date : 2003-06-05
Soliton Equations And Their Algebro Geometric Solutions Volume 1 1 1 Dimensional Continuous Models written by Fritz Gesztesy and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-05 with Mathematics categories.
The focus of this book is on algebro-geometric solutions of completely integrable nonlinear partial differential equations in (1+1)-dimensions, also known as soliton equations. Explicitly treated integrable models include the KdV, AKNS, sine-Gordon, and Camassa-Holm hierarchies as well as the classical massive Thirring system. An extensive treatment of the class of algebro-geometric solutions in the stationary as well as time-dependent contexts is provided. The formalism presented includes trace formulas, Dubrovin-type initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses techniques from the theory of differential equations, spectral analysis, and elements of algebraic geometry (most notably, the theory of compact Riemann surfaces). The presentation is rigorous, detailed, and self-contained, with ample background material provided in various appendices. Detailed notes for each chapter together with an exhaustive bibliography enhance the presentation offered in the main text.
Period Mappings And Period Domains
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Author : James Carlson
language : en
Publisher: Cambridge University Press
Release Date : 2003-10-20
Period Mappings And Period Domains written by James Carlson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-20 with Mathematics categories.
The period matrix of a curve effectively describes how the complex structure varies; this is Torelli's theorem dating from the beginning of the nineteenth century. In the 1950s during the first revolution of algebraic geometry, attention shifted to higher dimensions and one of the guiding conjectures, the Hodge conjecture, got formulated. In the late 1960s and 1970s Griffiths, in an attempt to solve this conjecture, generalized the classical period matrices introducing period domains and period maps for higher-dimensional manifolds. He then found some unexpected new phenomena for cycles on higher-dimensional algebraic varieties, which were later made much more precise by Clemens, Voisin, Green and others. This 2003 book presents this development starting at the beginning: the elliptic curve. This and subsequent examples (curves of higher genus, double planes) are used to motivate the concepts that play a role in the rest of the book.