1. Basic commutative algebra 1 -- 2. Introduction to projective modules -- 3. Stably free modules -- 4. Serre's conjecture -- 5. Continuous vector bundles -- 6. Basic commutative algebra II -- 7. Splitting theorem and Lindel's proof -- 8. Regular rings -- 9. Number of generators -- 10. Curves as complete intersection -- A. Normality of E[subscript n] in GL[subscript n] -- B. Some homological algebra -- C. Complete intersections and connectedness
Summary
"This monograph tells the story of a philosophy of J.-P. Serre and his vision of relating that philosophy to problems in affine algebraic geometry. It gives a lucid presentation of the Quillen-Suslin theorem settling Serre's conjecture." "The book gives a comprehensive introduction to basic commutative algebra, together with the related methods from homological algebra, which will enable students who know only the fundamentals of algebra to enjoy the power of using these tools. At the same time, it also serves as a valuable reference for the research specialist and as potential course material."--Jacket
