K Theory Projective Modules And Complete Intersections
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Projective Modules And Complete Intersections
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Author : Satya Mandal
language : en
Publisher: Springer
Release Date : 2006-11-14
Projective Modules And Complete Intersections written by Satya Mandal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
In these notes on "Projective Modules and Complete Intersections" an account on the recent developments in research on this subject is presented. The author's preference for the technique of Patching isotopic isomorphisms due to Quillen, formalized by Plumsted, over the techniques of elementary matrices is evident here. The treatment of Basic Element theory here incorporates Plumstead's idea of the "generalized dimension functions." These notes are highly selfcontained and should be accessible to any graduate student in commutative algebra or algebraic geometry. They include fully self-contained presentations of the theorems of Ferrand-Szpiro, Cowsik-Nori and the techniques of Lindel.
Serre S Problem On Projective Modules
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Author : T.Y. Lam
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-17
Serre S Problem On Projective Modules written by T.Y. Lam and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-17 with Mathematics categories.
“Serre’s Conjecture”, for the most part of the second half of the 20th century, - ferred to the famous statement made by J. -P. Serre in 1955, to the effect that one did not know if ?nitely generated projective modules were free over a polynomial ring k[x ,. . . ,x], where k is a ?eld. This statement was motivated by the fact that 1 n the af?ne scheme de?ned by k[x ,. . . ,x] is the algebro-geometric analogue of 1 n the af?ne n-space over k. In topology, the n-space is contractible, so there are only trivial bundles over it. Would the analogue of the latter also hold for the n-space in algebraic geometry? Since algebraic vector bundles over Speck[x ,. . . ,x] corre- 1 n spond to ?nitely generated projective modules over k[x ,. . . ,x], the question was 1 n tantamount to whether such projective modules were free, for any base ?eld k. ItwasquiteclearthatSerreintendedhisstatementasanopenproblemintheshe- theoretic framework of algebraic geometry, which was just beginning to emerge in the mid-1950s. Nowhere in his published writings had Serre speculated, one way or another, upon the possible outcome of his problem. However, almost from the start, a surmised positive answer to Serre’s problem became known to the world as “Serre’s Conjecture”. Somewhat later, interest in this “Conjecture” was further heightened by the advent of two new (and closely related) subjects in mathematics: homological algebra, and algebraic K-theory.
Leavitt Path Algebras And Classical K Theory
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Author : A. A. Ambily
language : en
Publisher: Springer Nature
Release Date : 2020-01-17
Leavitt Path Algebras And Classical K Theory written by A. A. Ambily and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-17 with Mathematics categories.
The book offers a comprehensive introduction to Leavitt path algebras (LPAs) and graph C*-algebras. Highlighting their significant connection with classical K-theory—which plays an important role in mathematics and its related emerging fields—this book allows readers from diverse mathematical backgrounds to understand and appreciate these structures. The articles on LPAs are mostly of an expository nature and the ones dealing with K-theory provide new proofs and are accessible to interested students and beginners of the field. It is a useful resource for graduate students and researchers working in this field and related areas, such as C*-algebras and symbolic dynamics.
Polytopes Rings And K Theory
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Author : Winfried Bruns
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-12
Polytopes Rings And K Theory written by Winfried Bruns and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-12 with Mathematics categories.
This book examines interactions of polyhedral discrete geometry and algebra. What makes this book unique is the presentation of several central results in all three areas of the exposition - from discrete geometry, to commutative algebra, and K-theory.
Algebraic K Theory The Homotopy Approach Of Quillen And An Approach From Commutative Algebra
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Author : Satya Mandal
language : en
Publisher: World Scientific
Release Date : 2023-06-22
Algebraic K Theory The Homotopy Approach Of Quillen And An Approach From Commutative Algebra written by Satya Mandal and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-22 with Mathematics categories.
In this book the author takes a pedagogic approach to Algebraic K-theory. He tried to find the shortest route possible, with complete details, to arrive at the homotopy approach of Quillen [Q] to Algebraic K-theory, with a simple goal to produce a self-contained and comprehensive pedagogic document in Algebraic K-theory, that is accessible to upper level graduate students. That is precisely what this book faithfully executes and achieves.The contents of this book can be divided into three parts — (1) The main body (Chapters 2-8), (2) Epilogue Chapters (Chapters 9, 10, 11) and (3) the Background and preliminaries (Chapters A, B, C, 1). The main body deals with Quillen's definition of K-theory and the K-theory of schemes. Chapters 2, 3, 5, 6, and 7 provide expositions of the paper of Quillen [Q], and chapter 4 is on agreement of Classical K-theory and Quillen K-theory. Chapter 8 is an exposition of the work of Swan [Sw1] on K-theory of quadrics.The Epilogue chapters can be viewed as a natural progression of Quillen's work and methods. These represent significant benchmarks and include Waldhausen K-theory, Negative K-theory, Hermitian K-theory, 𝕂-theory spectra, Grothendieck-Witt theory spectra, Triangulated categories, Nori-Homotopy and its relationships with Chow-Witt obstructions for projective modules. In most cases, the proofs are improvisation of methods of Quillen [Q].The background, preliminaries and tools needed in chapters 2-11, are developed in chapters A on Category Theory and Exact Categories, B on Homotopy, C on CW Complexes, and 1 on Simplicial Sets.
Projective Modules And Complete Intersections
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Author : Satya Mandal
language : en
Publisher:
Release Date : 2014-01-15
Projective Modules And Complete Intersections written by Satya Mandal and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
K Theory Projective Modules And Complete Intersections
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Author : Benjamin Parker Nicholson
language : en
Publisher:
Release Date : 1998
K Theory Projective Modules And Complete Intersections written by Benjamin Parker Nicholson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
K Theory
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Author : Michael Atiyah
language : en
Publisher: CRC Press
Release Date : 2018-03-05
K Theory written by Michael Atiyah and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-05 with Mathematics categories.
These notes are based on the course of lectures I gave at Harvard in the fall of 1964. They constitute a self-contained account of vector bundles and K-theory assuming only the rudiments of point-set topology and linear algebra. One of the features of the treatment is that no use is made of ordinary homology or cohomology theory. In fact, rational cohomology is defined in terms of K-theory.The theory is taken as far as the solution of the Hopf invariant problem and a start is mode on the J-homomorphism. In addition to the lecture notes proper, two papers of mine published since 1964 have been reproduced at the end. The first, dealing with operations, is a natural supplement to the material in Chapter III. It provides an alternative approach to operations which is less slick but more fundamental than the Grothendieck method of Chapter III, and it relates operations and filtration. Actually, the lectures deal with compact spaces, not cell-complexes, and so the skeleton-filtration does not figure in the notes. The second paper provides a new approach to K-theory and so fills an obvious gap in the lecture notes.
K Theory In Algebra Analysis And Topology
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Author : Guillermo Cortiñas
language : en
Publisher: American Mathematical Soc.
Release Date : 2020
K Theory In Algebra Analysis And Topology written by Guillermo Cortiñas and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Education categories.
This volume contains the proceedings of the ICM 2018 satellite school and workshop K-theory conference in Argentina. The school was held from July 16–20, 2018, in La Plata, Argentina, and the workshop was held from July 23–27, 2018, in Buenos Aires, Argentina. The volume showcases current developments in K-theory and related areas, including motives, homological algebra, index theory, operator algebras, and their applications and connections. Papers cover topics such as K-theory of group rings, Witt groups of real algebraic varieties, coarse homology theories, topological cyclic homology, negative K-groups of monoid algebras, Milnor K-theory and regulators, noncommutative motives, the classification of C∗-algebras via Kasparov's K-theory, the comparison between full and reduced C∗-crossed products, and a proof of Bott periodicity using almost commuting matrices.
Algebra K Theory Groups And Education
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Author : Hyman Bass
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Algebra K Theory Groups And Education written by Hyman Bass and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This volume includes expositions of key developments over the past four decades in commutative and non-commutative algebra, algebraic $K$-theory, infinite group theory, and applications of algebra to topology. Many of the articles are based on lectures given at a conference at Columbia University honoring the 65th birthday of Hyman Bass. Important topics related to Bass's mathematical interests are surveyed by leading experts in the field. Of particular note is a professional autobiography of Professor Bass, and an article by Deborah Ball on mathematical education. The range of subjects covered in the book offers a convenient single source for topics in the field.