Serre’s Problem on Projective Modules

• Main Author: Lam, Tsit Yuen (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Associative rings.; Rings (Algebra).; Commutative algebra.; Commutative rings.; Commutative Rings and Algebras.; Associative Rings and Algebras.

“Serre’s Conjecture”, for the most part of the second half of the 20th century, - ferred to the famous statement made by J. -P. Serre in 1955, to the effect that one did not know if ?nitely generated projective modules were free over a polynomial ring k[x ,. . . ,x], where k is a ?eld. This statemen...

Table of Contents:

• 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.