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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Bibliographic Details
Main Author: Mumford, David
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1988.
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.