Algebraic K-Theory: The Homotopy Approach of Quillen and an Approach from Commutative Algebra - Couverture rigide

Mandal, Satya

Couverture rigide

ISBN 10 : 9811269386 ISBN 13 : 9789811269387

Editeur : World Scientific Publishing Co Pte Ltd, 2023

Synopsis

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.

A propos du livre

À propos de l'auteur

Satya Manda joined University of Kansas in 1988 and currently holds a position of a professor. He completed his graduate studies in Indian Statistical Institute, Kolkata and Tata Institute of Fundamental Research, Mumbai. He completed his PhD under the supervision of Amit Roy in Tata Institute and got his degree in 1985. He spent the year 1983–84 as a Wissenschaftliche Hilfskraft (Research Assistant) in Universität Regensburg, Germany under the supervision of Earnst Kunz. He spent the year 1987–1988 in Mathematical Sciences Research Institute (MSRI), Berkeley, as a Postdoctoral Fellow.

The author published nearly fifty papers. This includes a book published in 1997. He gave numerous talks in national and international conferences. He has been active with experimentation with online pedagogy, since the inception of internet around 2000. He served his department in the capacity of the Chairman of the department.

Détails de l'édition

• Éditeur: World Scientific Publishing Co Pte Ltd
• Date d'édition: 2023
• Langue: anglais
• ISBN 10: 9811269386
• ISBN 13: 9789811269387
• Reliure: Relié
• Nombre de pages: 680
• Coordonnées du fabricant: non disponible
• Personne responsable: gpsr@libri.de; gpsr@libri.de; ; Europaallee 1; Bad Hersfeld; 36244; Allemagne