Algebraic K theory The Homotopy Approach Of Quillen And An Approach From Commutative Algebra is popular PDF and ePub book, written by Satya Mandal in 2023-06-22, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Algebraic K theory The Homotopy Approach Of Quillen And An Approach From Commutative Algebra can be Read Online from any device for your convenience.
Algebraic K theory The Homotopy Approach Of Quillen And An Approach From Commutative Algebra Book PDF Summary
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.
Detail Book of Algebraic K theory The Homotopy Approach Of Quillen And An Approach From Commutative Algebra PDF
- Author : Satya Mandal
- Release : 22 June 2023
- Publisher : World Scientific
- ISBN : 9789811269400
- Genre : Mathematics
- Total Page : 680 pages
- Language : English
- PDF File Size : 18,5 Mb
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