Buch, Englisch, 341 Seiten, Format (B × H): 156 mm x 236 mm, Gewicht: 511 g
Reihe: Modern Birkhäuser Classics
Buch, Englisch, 341 Seiten, Format (B × H): 156 mm x 236 mm, Gewicht: 511 g
Reihe: Modern Birkhäuser Classics
ISBN: 978-0-8176-4736-0
Verlag: Birkhauser Boston
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. This new 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 applications 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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Algebra Homologische Algebra
- Mathematik | Informatik Mathematik Topologie Algebraische Topologie
- Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
- Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
- Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
Weitere Infos & Material
“Classical” K-Theory.- The Plus Construction.- The Classifying Space of a Small Category.- Exact Categories and Quillen’s Q-Construction.- The K-Theory of Rings and Schemes.- Proofs of the Theorems of Chapter 4.- Comparison of the Plus and Q-Constructions.- The Merkurjev-Suslin Theorem.- Localization for Singular Varieties.
