Serre's Conjecture [Paperback]

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. 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. Foundations.- The classical results on serres conjecture.- Two elementary proofs of serres conjecture.- Horrocks theorem.- Quillens method.- The quadratic analogue of serres conjecture.Springer Book Archives