The red book of varieties and schemes: : includes the Michigan Lectures (1974) on curves and their Jacobians/
David Mumford
- 2nd expanded ed.
- Berlin: Springer, 1999.
- x, 304 p. : ill. ; 24 cm.
- (Lecture notes in mathematics), 1358 .
I. Varieties -- 1. Some algebra -- 2. Irreducible algebraic sets -- 3. Definition of a morphism -- 4. Sheaves and affine varieties -- 5. Definition of prevarieties and morphisms -- 6. Products and the Hausdorff Axiom -- 7. Dimension -- 8. The fibres of a morphism -- 9. Complete varieties -- 10. Complex varieties -- II. Preschemes -- 1. Spec (R) -- 2. The category of preschemes -- 3. Varieties and preschemes -- 4. Fields of definition -- 5. Closed subpreschemes -- 6. The functor of points of a prescheme -- 7. Proper morphisms and finite morphisms -- 8. Specialization -- III. Local Properties of Schemes -- 1. Quasi-coherent modules -- 2. Coherent modules -- 3. Tangent cones -- 4. Non-singularity and differentials -- 5. Etale morphisms -- 6. Uniformizing parameters -- 7. Non-singularity and the UFD property -- 8. Normal varieties and normalization -- 9. Zariski's Main Theorem -- 10. Flat and smooth morphisms -- App. Curves and Their Jacobians -- Lecture I. What is a Curve and How Explicitly Can We Describe Them? -- Lecture II. The Moduli Space of Curves: Definition, Coordinatization, and Some Properties -- Lecture III. How Jacobians and Theta Functions Arise -- Lecture IV. The Torelli Theorem and the Schottky Problem -- Survey of Work on the Schottky Problem up to 1996 / Enrico Arbarello -- References: The Red Book of Varieties and Schemes -- Guide to the Literature and References: Curves and Their Jacobians -- Supplementary Bibliography on the Schottky Problem / Enrico Arbarello.