Algebraic Geometry: Part I: Schemes. With Examples and Exercises (Google eBook)

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Springer Science & Business Media, Aug 9, 2010 - Algebra - 619 pages
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Contents

Introduction
1
1 Prevarieties
7
2 Spectrum of a Ring
40
3 Schemes
66
4 Fiber products
93
5 Schemes over fields
118
6 Local Properties of Schemes
145
7 Quasicoherent modules
169
14 Flat morphisms and dimension
423
15 Onedimensional schemes
485
16 Examples
503
A The language of categories
541
B Commutative Algebra
547
C Permanence for properties of morphisms of schemes
573
D Relations between properties of morphisms of schemes
576
E Constructible and open properties
578

8 Representable Functors
205
9 Separated morphisms
226
10 Finiteness Conditions
241
11 Vector bundles
286
12 Affine and proper morphisms
320
13 Projective morphisms
366
Bibliography
583
Detailed List of Contents
588
Index of Symbols
598
Index
602
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