{"product_id":"algebraic-k-theory-9789811269387-new","title":"Algebraic K-Theory","description":"\u003cp\u003eIn this book the author takes a pedagogic approach to Algebraic \u003cem\u003eK\u003c\/em\u003e-theory. He tried to find the shortest route possible, with complete details, to arrive at the homotopy approach of Quillen [Q] to Algebraic \u003cem\u003eK\u003c\/em\u003e-theory, with a simple goal to produce a self-contained and comprehensive pedagogic document in Algebraic \u003cem\u003eK\u003c\/em\u003e-theory, that is accessible to upper level graduate students. That is precisely what this book faithfully executes and achieves.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe 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 \u003cem\u003eK\u003c\/em\u003e-theory and the \u003cem\u003eK\u003c\/em\u003e-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 \u003cem\u003eK\u003c\/em\u003e-theory and Quillen \u003cem\u003eK\u003c\/em\u003e-theory. Chapter 8 is an exposition of the work of Swan [Sw1] on \u003cem\u003eK\u003c\/em\u003e-theory of quadrics.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe Epilogue chapters can be viewed as a natural progression of Quillen's work and methods. These represent significant benchmarks and include Waldhausen \u003cem\u003eK\u003c\/em\u003e-theory, Negative \u003cem\u003eK\u003c\/em\u003e-theory, Hermitian \u003cem\u003eK\u003c\/em\u003e-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].\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe 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.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544198873378,"sku":"9789811269387-new","price":191.71,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789811269387.jpg?v=1776399965","url":"https:\/\/www.albakireads.com\/products\/algebraic-k-theory-9789811269387-new","provider":"AlbakiReads","version":"1.0","type":"link"}