Algebraic K-theory: The Homotopy Approach Of Quillen And An Approach From Commutative Algebra

Lingua: inglese

Editore: World Scientific Publishing Co Pte Ltd, SG, 2023

9811269386 / 9789811269387

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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, -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.…

Codice articolo LU-9789811269387

Titolo
Algebraic K-theory: The Homotopy Approach Of Quillen And An Approach From Commutative Algebra
Autore
Satya Mandal
Editore
World Scientific Publishing Co Pte Ltd, SG
Anno di pubblicazione
2023
Condizione
New
Rilegatura
Hardback
Lingua
inglese
ISBN 10
9811269386
ISBN 13
9789811269387
Dimensioni
15.24 x 3.66 x 22.86 cm

Rarewaves.com USA

London, London, Regno Unito

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Venditore AbeBooks dal 11 giugno 2025

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