Student Reading Seminar
Mumford, The Red Book of Varieties and Schemes
Chapter 1
- Section 1.1: Some algebra
- Section 1.2: Irreducible algebraic sets
- Section 1.3: Definition of a morphism
- Section 1.4: Sheaves and affine varieties
- Section 1.5: Definition of prevarieties and morphisms
- Section 1.6: Products and the Hausdorff Axiom
- Section 1.7: Dimension
- Section 1.8: The fibres of a morphism
- Section 1.9: Complete varieties
- Section 1.10: Complex varieties
Chapter 2
- Section 2.1: Spec(R)
- Section 2.2: The category of preschemes
- Section 2.3: Varieties and preschemes
- Section 2.4: Fields of definition
- Section 2.5: Closed subpreschemes
- Section 2.6: The functor of points of a prescheme
- Section 2.7: Proper morphisms and finite morphisms
- Section 2.8: Specialization
Chapter 3
- Section 3.1: Quasi-coherent modules
- Section 3.2: Coherent modules
- Section 3.3: Tangent cones