The Red Book of Varieties and Schemes /
"The book under review is a reprint of Mumford's famous Harvard lecture notes, widely used by the few past generations of algebraic geometers. Springer-Verlag has done the mathematical community a service by making these notes available once again.... The informal style and frequency of ex...
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| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
1988.
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| Series: | Lecture notes in mathematics (Springer-Verlag) ;
1358. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Varieties
- Some algebra
- Irreducible algebraic sets
- Definition of a morphism: I
- Sheaves and affine varieties
- Definition of prevarieties and morphism
- Products and the Hausdorff Axiom
- Dimension
- The fibres of a morphism
- Complete varieties
- Complex varieties
- Preschemes
- Spec (R)
- The category of preschemes
- Varieties are preschemes
- Fields of definition
- Closed subpreschemes
- The functor of points of a prescheme
- Proper morphisms and finite morphisms
- Specialization
- Local Properties of Schemes
- Quasi-coherent modules
- Coherent modules
- Tangent cones
- Non-singularity and differentials
- Étale morphisms
- Uniformizing parameters
- Non-singularity and the UFD property
- Normal varieties and normalization
- Zariski's Main Theorem
- Flat and smooth morphisms.