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portada Algebraic K-Theory: The Homotopy Approach of Quillen and an Approach from Commutative Algebra (in English)
Type
Physical Book
Language
English
Pages
680
Format
Hardcover
Dimensions
22.9 x 15.2 x 3.7 cm
Weight
1.07 kg.
ISBN13
9789811269387

Algebraic K-Theory: The Homotopy Approach of Quillen and an Approach from Commutative Algebra (in English)

Satya Mandal (Author) · World Scientific Publishing Company · Hardcover

Algebraic K-Theory: The Homotopy Approach of Quillen and an Approach from Commutative Algebra (in English) - Mandal, Satya

Physical Book

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Synopsis "Algebraic K-Theory: The Homotopy Approach of Quillen and an Approach from Commutative Algebra (in English)"

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.

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The book is written in English.
The binding of this edition is Hardcover.

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