66 Morphisms of Algebraic Spaces
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Section 66.1: Introduction
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Section 66.2: Conventions
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Section 66.3: Properties of representable morphisms
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Section 66.4: Separation axioms
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Section 66.5: Surjective morphisms
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Section 66.6: Open morphisms
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Section 66.7: Submersive morphisms
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Section 66.8: Quasi-compact morphisms
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Section 66.9: Universally closed morphisms
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Section 66.10: Monomorphisms
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Section 66.11: Pushforward of quasi-coherent sheaves
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Section 66.12: Immersions
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Section 66.13: Closed immersions
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Section 66.14: Closed immersions and quasi-coherent sheaves
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Section 66.15: Supports of modules
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Section 66.16: Scheme theoretic image
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Section 66.17: Scheme theoretic closure and density
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Section 66.18: Dominant morphisms
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Section 66.19: Universally injective morphisms
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Section 66.20: Affine morphisms
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Section 66.21: Quasi-affine morphisms
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Section 66.22: Types of morphisms étale local on source-and-target
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Section 66.23: Morphisms of finite type
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Section 66.24: Points and geometric points
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Section 66.25: Points of finite type
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Section 66.26: Nagata spaces
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Section 66.27: Quasi-finite morphisms
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Section 66.28: Morphisms of finite presentation
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Section 66.29: Constructible sets
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Section 66.30: Flat morphisms
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Section 66.31: Flat modules
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Section 66.32: Generic flatness
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Section 66.33: Relative dimension
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Section 66.34: Morphisms and dimensions of fibres
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Section 66.35: The dimension formula
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Section 66.36: Syntomic morphisms
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Section 66.37: Smooth morphisms
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Section 66.38: Unramified morphisms
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Section 66.39: Étale morphisms
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Section 66.40: Proper morphisms
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Section 66.41: Valuative criteria
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Section 66.42: Valuative criterion for universal closedness
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Section 66.43: Valuative criterion of separatedness
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Section 66.44: Valuative criterion of properness
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Lemma 66.44.1: Valuative criterion for properness
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Section 66.45: Integral and finite morphisms
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Section 66.46: Finite locally free morphisms
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Section 66.47: Rational maps
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Section 66.48: Relative normalization of algebraic spaces
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Section 66.49: Normalization
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Section 66.50: Separated, locally quasi-finite morphisms
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Section 66.51: Applications
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Section 66.52: Zariski's Main Theorem (representable case)
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Section 66.53: Universal homeomorphisms