Algebraic K-theory: The Homotopy Approach Of Quillen And An Approach From Commutative Algebra
Regular price
€192.20
14 days return policy
Shipping & Delivery
-theory
A01=Satya Mandal
Abelian Category
Acyclic Complex
Additive Category
Adjoint Functor
Author_Satya Mandal
Calculus of Fractions
Category=PBF
Cell Decomposition
Cellural Approximation
Chow Group
Chow-Witt Group
Classifying Spaces
Clifford Algebra
Cofibration
Cofinality
Complicial Exact Category
Compression Criteria
Connecting Homomorphism
Connective Spectrum
Contrctible Spaces
CW Complex
Cylinder
Derived Category
Dg Category
Edgewise Subdivision
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equivalnece of Categories
Essentially Surjective
Exact Category
Exact Sequence
Excision
Filtering Limit
Function Space
Fundamental Ideal
Geometric Realization
Gersten Complex
Gersten Witt Complex
Grothendieck
Grothendieck Group
Groups
HEP
Hermitian K-theory
Higher K-theory
Homotopy Fiber
Homotopy Fibration
Hyperbolic Space
Idempotent Completion
Kan Extension
Lagrangian
Latching Set
Localization
Loop Space
Mapping Cylinder
Metabolic Space
Monoidal Category
Morita Equivalence
Morita Exact
Nerve of a Category
Non Connective A?A?AoA
Non Connective K-theory
Non Connective ð•‚-theory
Nori Homotopy
Ore Condition
Perfect Complex
Pretriangualted Dg Categories
Projection Formula
Pullback
Pushforward
Quasi Fibration
Quasi Projective Scheme
Quillen K-theory
Quotient of Categories
Regular Rings
Resolving Categories
Rings
Saturation Axiom
Schemes
Semisimple Object
Serre Category
Shear Map
Shifted Duality
Shifted Witt Groups
Simple Object
Simplical Set
Simplicial Sets
Skeleton
Spectra
Spectral Sequence
Suslin
Suspension
Symmetric Form
Theorem A-B
Transfer Map
Triangualted Category
Verdier Quotient
Voevodsky
Waldhausen Categories
Weak Equivalance
Weibel
Whitehead Group
Zariski Topology
Product details
- ISBN 9789811269387
- Publication Date: 18 Jul 2023
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
Secure
checkout
Fast Shipping
Easy returns
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.
