Serre's Conjecture

From the Preface: "I felt it would be useful for graduate students to see a detailed account of the sequence of mathematical developments which was inspired by the Conjecture, and which ultimately led to its full solution.... I offered a course on Serre's Conjecture to a small group of graduate students in January, 1977 [at the University of California, Berkeley] one year after its solution by Quillen and Suslin. My course was taught very much in the spirit of a mathematical 'guided tour'. Volunteering as the guide, I took upon myself the task of charting a route through all the beautiful mathematics surrounding the main problem to be treated; the 'guide' then leads his audience through the route, on to the destination, pointing out the beautiful sceneries and historical landmarks along the way."

Klappentext

From the Preface: "I felt it would be useful for graduate students to see a detailed account of the sequence of mathematical developments which was inspired by the Conjecture, and which ultimately led to its full solution.... I offered a course on Serre's Conjecture to a small group of graduate students in January, 1977 [at the University of California, Berkeley] one year after its solution by Quillen and Suslin. My course was taught very much in the spirit of a mathematical 'guided tour'. Volunteering as the guide, I took upon myself the task of charting a route through all the beautiful mathematics surrounding the main problem to be treated; the 'guide' then leads his audience through the route, on to the destination, pointing out the beautiful sceneries and historical landmarks along the way." TOC:Preface.- Introduction.- Foundations.- The "Classical" Results on Serre's Conjecture.- Two Elementary Proofs of Serre's Conjecture.- Horrocks' Theorem.- Quillen's Method.- The Quadratic Analogue of Serre's Conjecture.- Appendix on Complete Intersections.- References.- Notations.- Index

Inhalt
Foundations.- The "classical" results on serre's conjecture.- Two elementary proofs of serre's conjecture.- Horrocks' theorem.- Quillen's method.- The quadratic analogue of serre's conjecture.