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\end{equation*}
27 Properties of Schemes
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Section 27.1: Introduction
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Section 27.2: Constructible sets
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Section 27.3: Integral, irreducible, and reduced schemes
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Section 27.4: Types of schemes defined by properties of rings
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Section 27.5: Noetherian schemes
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Section 27.6: Jacobson schemes
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Section 27.7: Normal schemes
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Section 27.8: Cohen-Macaulay schemes
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Section 27.9: Regular schemes
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Section 27.10: Dimension
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Section 27.11: Catenary schemes
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Section 27.12: Serre's conditions
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Section 27.13: Japanese and Nagata schemes
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Section 27.14: The singular locus
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Section 27.15: Local irreducibility
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Section 27.16: Characterizing modules of finite type and finite presentation
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Section 27.17: Sections over principal opens
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Section 27.18: Quasi-affine schemes
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Section 27.19: Flat modules
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Section 27.20: Locally free modules
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Section 27.21: Locally projective modules
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Section 27.22: Extending quasi-coherent sheaves
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Section 27.23: Gabber's result
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Section 27.24: Sections with support in a closed subset
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Section 27.25: Sections of quasi-coherent sheaves
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Section 27.26: Ample invertible sheaves
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Section 27.27: Affine and quasi-affine schemes
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Section 27.28: Quasi-coherent sheaves and ample invertible sheaves
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Section 27.29: Finding suitable affine opens