37 More on Morphisms
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Section 37.1: Introduction
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Section 37.2: Thickenings
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Section 37.3: Morphisms of thickenings
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Section 37.4: Picard groups of thickenings
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Section 37.5: First order infinitesimal neighbourhood
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Section 37.6: Formally unramified morphisms
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Section 37.7: Universal first order thickenings
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Section 37.8: Formally étale morphisms
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Section 37.9: Infinitesimal deformations of maps
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Section 37.10: Infinitesimal deformations of schemes
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Section 37.11: Formally smooth morphisms
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Section 37.12: Smoothness over a Noetherian base
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Section 37.13: The naive cotangent complex
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Section 37.14: Pushouts in the category of schemes, I
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Section 37.15: Openness of the flat locus
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Section 37.16: Critère de platitude par fibres
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Section 37.17: Normalization revisited
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Lemma 37.17.1
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Lemma 37.17.2: Normalization commutes with smooth base change
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Lemma 37.17.3: Normalization and smooth morphisms
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Lemma 37.17.4: Normalization and henselization
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Section 37.18: Normal morphisms
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Section 37.19: Regular morphisms
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Section 37.20: Cohen-Macaulay morphisms
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Section 37.21: Slicing Cohen-Macaulay morphisms
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Section 37.22: Generic fibres
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Section 37.23: Relative assassins
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Section 37.24: Reduced fibres
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Section 37.25: Irreducible components of fibres
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Section 37.26: Connected components of fibres
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Section 37.27: Connected components meeting a section
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Section 37.28: Dimension of fibres
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Section 37.29: Theorem of the cube
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Section 37.30: Limit arguments
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Section 37.31: Étale neighbourhoods
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Section 37.32: Étale neighbourhoods and Artin approximation
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Section 37.33: Étale neighbourhoods and branches
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Section 37.34: Slicing smooth morphisms
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Section 37.35: Finite free locally dominates étale
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Section 37.36: Étale localization of quasi-finite morphisms
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Section 37.37: Étale localization of integral morphisms
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Section 37.38: Zariski's Main Theorem
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Section 37.39: Applications of Zariski's Main Theorem, I
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Section 37.40: Applications of Zariski's Main Theorem, II
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Section 37.41: Application to morphisms with connected fibres
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Section 37.42: Application to the structure of finite type morphisms
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Section 37.43: Application to the fppf topology
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Section 37.44: Quasi-projective schemes
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Section 37.45: Projective schemes
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Section 37.46: Proj and Spec
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Section 37.47: Closed points in fibres
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Section 37.48: Stein factorization
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Section 37.49: Descending separated locally quasi-finite morphisms
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Section 37.50: Relative finite presentation
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Section 37.51: Relative pseudo-coherence
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Section 37.52: Pseudo-coherent morphisms
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Section 37.53: Perfect morphisms
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Section 37.54: Local complete intersection morphisms
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Section 37.55: Exact sequences of differentials and conormal sheaves
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Section 37.56: Weakly étale morphisms
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Section 37.57: Reduced fibre theorem
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Section 37.58: Ind-quasi-affine morphisms
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Section 37.59: Pushouts in the category of schemes, II
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Section 37.60: Relative morphisms
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Section 37.61: Characterizing pseudo-coherent complexes, III
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Section 37.62: Descent finiteness properties of complexes
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Section 37.63: Relatively perfect objects
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Section 37.64: Contracting rational curves
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Section 37.65: Affine stratifications
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Section 37.66: Universally open morphisms
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Section 37.67: Weightings
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Section 37.68: More on weightings
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Section 37.69: Weightings and affine stratification numbers