Table of Contents

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   Book Overview
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   Chapter 1 Some algebra
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   Chapter 2 Irreducible algebraic sets
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   Chapter 3 Definition of a morphism: I
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   Chapter 4 Sheaves and affine varieties
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   Chapter 5 Definition of prevarieties and morphism
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   Chapter 6 Products and the Hausdorff Axiom
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   Chapter 7 Dimension
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   Chapter 8 The fibres of a morphism
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    Chapter 9 Complete varieties
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    Chapter 10 Complex varieties
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    Chapter 11 Spec (R)
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    Chapter 12 The category of preschemes
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    Chapter 13 Varieties are preschemes
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    Chapter 14 Fields of definition
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    Chapter 15 Closed subpreschemes
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    Chapter 16 The functor of points of a prescheme
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    Chapter 17 Proper morphisms and finite morphisms
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    Chapter 18 Specialization
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    Chapter 19 Quasi-coherent modules
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    Chapter 20 Coherent modules
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    Chapter 21 Tangent cones
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    Chapter 22 Non-singularity and differentials
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    Chapter 23 Étale morphisms
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    Chapter 24 Uniformizing parameters
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    Chapter 25 Non-singularity and the UFD property
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    Chapter 26 Normal varieties and normalization
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    Chapter 27 Zariski’s Main Theorem
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    Chapter 28 Flat and smooth morphisms