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＜E-Book＞
The Red Book of Varieties and Schemes / by David Mumford
(Lecture Notes in Mathematics. ISSN:16179692 ; 1358)

Edition	1st ed. 1988.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	1988
Size	V, 315 p. 13 illus : online resource
Authors	*Mumford, David author SpringerLink (Online service)
Subjects	LCSH:Algebraic geometry FREE:Algebraic Geometry
Notes	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 "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 examples make the book an excellent text." (Mathematical Reviews) HTTP:URL=https://doi.org/10.1007/978-3-662-21581-4

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