Description
Book SynopsisAn invaluable summary of research work done in the period from 1978 to the present
Trade ReviewFrom 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)
Table of Contentsto 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.
