Serre’s Conjecture

T. Y. Lam (auth.)9780387086576, 0-387-08657-9

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.”

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Table of contents :
Foundations….Pages 1-44
The “classical” results on serre’s conjecture….Pages 45-78
Two elementary proofs of serre’s conjecture….Pages 79-95
Horrocks’ theorem….Pages 97-121
Quillen’s method….Pages 123-165
The quadratic analogue of serre’s conjecture….Pages 167-204