Author | Mumford, David. author |
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Title | The Red Book of Varieties and Schemes [electronic resource] / by David Mumford |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1988 |
Connect to | http://dx.doi.org/10.1007/978-3-662-21581-4 |
Descript | V, 315 p. 13 illus. online resource |
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 -- รtale morphisms -- Uniformizing parameters -- Non-singularity and the UFD property -- Normal varieties and normalization -- Zariskiโs Main Theorem -- Flat and smooth morphisms