Serre's Problem on Projective Modules

Inbunden, Engelska, 2006

Av T.Y. Lam, T. y. Lam

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This book covers the area of "Serre's Problem on Projective Modules" quite thoroughly, and from very many different angles. It presents the broadest and most comprehensive view available in the literature on the mathematics of "Serre's Conjecture", its history, its different solutions, and the important subsequent developments. Based on an earlier version of this book (Lecture Notes in Mathematics Vol. 635) this volume has been considerably expanded. Different segments of the material have been added to the existing chapters of the original book and two completely new chapters one for example on Suslin's important work on the K1 analogue of Serre's Conjecture. The second is a new chapter which surveys the subsequent developments in many acts and ramifications on Serre's Conjecture that took place in the "post Quillen-Suslin era". This book is an invaluable summary of research work done in the period from 1978 to the present.

Produktinformation

Utgivningsdatum2006-05-05
Mått178 x 254 x undefined mm
FormatInbunden
SpråkEngelska
SerieSpringer Monographs in Mathematics
Antal sidor404
FörlagSpringer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN9783540233176

Tillhör följande kategorier

Algebra inom Naturvetenskap och teknik

to Serre’s Conjecture: 1955–1976.- Foundations.- The “Classical” Results on Serre’s Conjecture.- The Basic Calculus of Unimodular Rows.- Horrocks’ Theorem.- Quillen’s Methods.- K1-Analogue of Serre’s Conjecture.- The Quadratic Analogue of Serre’s Conjecture.- References for Chapters I–VII.- Appendix: Complete Intersections and Serre’s Conjecture.- New Developments (since 1977).- References for Chapter VIII.

From the reviews: "It is a full-fledged advanced course on themes in higher algebra suited for a specialized graduate seminar, a research seminar, and of course, self-study by an aspiring researcher. ... Serre's Problem on Projective Modules, is very clear and well written ... and quickly gets the reader properly air-borne. ... the pay-off is huge: this is fantastic stuff. ... is a superb book. It's highly recommended." (Michael Berg, MathDL, March, 2007) "The book starts with the basics of projective modules and the K0 and K1 groups, and then gives the classical, partial results about Serre's conjecture. ... This well-written book is the definitive treatment of 'Serre's conjecture' - its history, solution, and generalizations - and will be of interest to both beginning graduate students and advanced researchers in this field." (David F. Anderson, Zentralblatt MATH, Vol. 1101 (3), 2007) "Lam has done a magnificent job of organizing the mated al and presenting complete proofs of all the results directly connected with Sen-e's problem. ... The references are complete and make the book a very valuable reference even for experts in the field... It will be very useful to students wishing to learn about projective modules ... . This is definitely a book that anyone ... interested in projective modules should have on his or her shelf!" (Richard G. Swan, Bulletin of the American Mathematical Society, Vol. 45 (3), July, 2008)