Algebraic K-Theory: v. 90 - Rilegato

Srinivas, V.

Rilegato

ISBN 10: 0817637028 ISBN 13: 9780817637026

Casa editrice: Birkhauser, 1993

Riassunto

Algebraic K-Theory is an active area of research that has connections with algebra, algebraic geometry, topology, an number theory. Based on notes from lectures given by the author at the Tata Institute in Bombay , this revised edition provides an introduction to higher K-theory for professional mathematicians and graduate students. It presumes a limited background in topology and thus provides the necessary proofs of topological results, and focuses on applications in algebra and algebraic geometry. A major part of the book is devoted to a detailed exposition of the ideas of Quillen as contained in the now classic papers 'Higher Algebraic K-theory, I, II." Beyond this, two applications are given: to the theorem of Mercurjev and Suslin relating K2 and the Brauer group of a field (given in this Second Edition in a simplified version); and to modules of finite length and recited projective dimension over the local ring of a normal surface singularity. These results lead the reader to some interesting conclusions regarding the Chow group of varieties. Appendices on topological results, results from algebraic geometry, category theory and exact couples are included, to make the exposition more self-contained.

Su questo libro

Dalla quarta di copertina

Algebraic K-Theory has become an increasingly active area of research. With its connections to algebra, algebraic geometry, topology, and number theory, it has implications for a wide variety of researchers and graduate students in mathematics. The book is based on lectures given at the author's home institution, the Tata Institute in Bombay, and elsewhere. A detailed appendix on topology was provided in the first edition to make the treatment accessible to readers with a limited background in topology. The second edition also includes an appendix on algebraic geometry that contains the required definitions and results needed to understand the core of the book; this makes the book accessible to a wider audience.

A central part of the book is a detailed exposition of the ideas of Quillen as contained in his classic papers "Higher Algebraic K-Theory, I, II." A more elementary proof of the theorem of Merkujev--Suslin is given in this edition; this makes the treatment of this topic self-contained. An application is also given to modules of finite length and finite projective dimension over the local ring of a normal surface singularity. These results lead the reader to some interesting conclusions regarding the Chow group of varieties.

 

"It is a pleasure to read this mathematically beautiful book..." ---WW.J. Julsbergen, Mathematics Abstracts

"The book does an admirable job of presenting the details of Quillen's work..." ---Mathematical Reviews

Dettagli dell?edizione

• Editore: Birkhauser
• Data di pubblicazione: 1993
• Lingua: Inglese
• ISBN 10: 0817637028
• ISBN 13: 9780817637026
• Rilegatura: Copertina rigida
• Numero di pagine: 341
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile