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School On Algebraic K Theory And Its Applications
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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 And Its Applications - Proceedings Of The School by : Hyman Bass
Download or read book Algebraic K-theory And Its Applications - Proceedings Of The School written by Hyman Bass and published by World Scientific. This book was released on 1999-03-12 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 2013-11-21 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis School on Algebraic K-theory and Its Applications by : Max Karoubi
Download or read book School on Algebraic K-theory and Its Applications written by Max Karoubi and published by . This book was released on 2003 with total page 554 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
Book Synopsis Transcendental Aspects of Algebraic Cycles by : S. Müller-Stach
Download or read book Transcendental Aspects of Algebraic Cycles written by S. Müller-Stach and published by Cambridge University Press. This book was released on 2004-04-20 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lecture notes for graduates or researchers wishing to enter this modern field of research.
Book Synopsis Algebraic K-Theory and its Geometric Applications by : Robert M.F. Moss
Download or read book Algebraic K-Theory and its Geometric Applications written by Robert M.F. Moss and published by Springer. This book was released on 2006-11-15 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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".
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 Motivic Homotopy Theory by : Bjorn Ian Dundas
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.
Book Synopsis Universal Algebra, Algebraic Logic, and Databases by : Boris Isaakovich Plotkin
Download or read book Universal Algebra, Algebraic Logic, and Databases written by Boris Isaakovich Plotkin and published by Boom Koninklijke Uitgevers. This book was released on 1994-01-31 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern algebra, which not long ago seemed to be a science divorced from real life, now has numerous applications. Many fine algebraic structures are endowed with meaningful contents. Now and then practice suggests new and unexpected structures enriching algebra. This does not mean that algebra has become merely a tool for applications. Quite the contrary, it significantly benefits from the new connections. The present book is devoted to some algebraic aspects of the theory of databases. It consists of three parts. The first part contains information about universal algebra, algebraic logic is the subject of the second part, and the third one deals with databases. The algebraic material of the flI'St two parts serves the common purpose of applying algebra to databases. The book is intended for use by mathematicians, and mainly by algebraists, who realize the necessity to unite theory and practice. It is also addressed to programmers, engineers and all potential users of mathematics who want to construct their models with the help of algebra and logic. Nowadays, the majority of professional mathematicians work in close cooperation with representatives of applied sciences and even industrial technology. It is neces sary to develop an ability to see mathematics in different particular situations. One of the tasks of this book is to promote the acquisition of such skills.
Book Synopsis An Introduction to K-Theory for C*-Algebras by : M. Rørdam
Download or read book An Introduction to K-Theory for C*-Algebras written by M. Rørdam and published by Cambridge University Press. This book was released on 2000-07-20 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a very elementary introduction to K-theory for C*-algebras, and is ideal for beginning graduate students.
Book Synopsis The Unity of Mathematics by : Pavel Etingof
Download or read book The Unity of Mathematics written by Pavel Etingof and published by Springer Science & Business Media. This book was released on 2007-05-31 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tribute to the vision and legacy of Israel Moiseevich Gel'fand Written by leading mathematicians, these invited papers reflect the unity of mathematics as a whole, with particular emphasis on the many connections among the fields of geometry, physics, and representation theory Topics include conformal field theory, K-theory, noncommutative geometry, gauge theory, representations of infinite-dimensional Lie algebras, and various aspects of the Langlands program
Book Synopsis Algebraic Geometry and Statistical Learning Theory by : Sumio Watanabe
Download or read book Algebraic Geometry and Statistical Learning Theory written by Sumio Watanabe and published by Cambridge University Press. This book was released on 2009-08-13 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sure to be influential, Watanabe's book lays the foundations for the use of algebraic geometry in statistical learning theory. Many models/machines are singular: mixture models, neural networks, HMMs, Bayesian networks, stochastic context-free grammars are major examples. The theory achieved here underpins accurate estimation techniques in the presence of singularities.
Download or read book Mixed Motives written by Marc Levine and published by American Mathematical Soc.. This book was released on 1998 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book combines foundational constructions in the theory of motives and results relating motivic cohomology to more explicit constructions. Prerequisite for understanding the work is a basic background in algebraic geometry. The author constructs and describes a triangulated category of mixed motives over an arbitrary base scheme. Most of the classical constructions of cohomology are described in the motivic setting, including Chern classes from higher $K$-theory, push-forward for proper maps, Riemann-Roch, duality, as well as an associated motivic homology, Borel-Moore homology and cohomology with compact supports.
Book Synopsis On the Class Number of Abelian Number Fields by : Helmut Hasse
Download or read book On the Class Number of Abelian Number Fields written by Helmut Hasse and published by Springer. This book was released on 2019-04-23 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this translation, the classic monograph Über die Klassenzahl abelscher Zahlkörper by Helmut Hasse is now available in English for the first time. The book addresses three main topics: class number formulas for abelian number fields; expressions of the class number of real abelian number fields by the index of the subgroup generated by cyclotomic units; and the Hasse unit index of imaginary abelian number fields, the integrality of the relative class number formula, and the class number parity. Additionally, the book includes reprints of works by Ken-ichi Yoshino and Mikihito Hirabayashi, which extend the tables of Hasse unit indices and the relative class numbers to imaginary abelian number fields with conductor up to 100. The text provides systematic and practical methods for deriving class number formulas, determining the unit index and calculating the class number of abelian number fields. A wealth of illustrative examples, together with corrections and remarks on the original work, make this translation a valuable resource for today’s students of and researchers in number theory.
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.
