100 Morphisms of Algebraic Stacks
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Section 100.1: Introduction
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Section 100.2: Conventions and abuse of language
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Section 100.3: Properties of diagonals
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Section 100.4: Separation axioms
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Section 100.5: Inertia stacks
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Section 100.6: Higher diagonals
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Section 100.7: Quasi-compact morphisms
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Section 100.8: Noetherian algebraic stacks
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Section 100.9: Affine morphisms
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Section 100.10: Integral and finite morphisms
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Section 100.11: Open morphisms
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Section 100.12: Submersive morphisms
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Section 100.13: Universally closed morphisms
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Section 100.14: Universally injective morphisms
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Section 100.15: Universal homeomorphisms
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Section 100.16: Types of morphisms smooth local on source-and-target
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Section 100.17: Morphisms of finite type
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Section 100.18: Points of finite type
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Section 100.19: Automorphism groups
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Section 100.20: Presentations and properties of algebraic stacks
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Section 100.21: Special presentations of algebraic stacks
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Section 100.22: The Deligne-Mumford locus
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Section 100.23: Locally quasi-finite morphisms
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Section 100.24: Quasi-finite morphisms
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Section 100.25: Flat morphisms
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Section 100.26: Flat at a point
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Section 100.27: Morphisms of finite presentation
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Section 100.28: Gerbes
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Section 100.29: Stratification by gerbes
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Section 100.30: The topological space of an algebraic stack
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Section 100.31: Existence of residual gerbes
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Section 100.32: Étale local structure
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Section 100.33: Smooth morphisms
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Section 100.34: Types of morphisms étale-smooth local on source-and-target
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Section 100.35: Étale morphisms
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Section 100.36: Unramified morphisms
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Section 100.37: Proper morphisms
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Section 100.38: Scheme theoretic image
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Section 100.39: Valuative criteria
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Section 100.40: Valuative criterion for second diagonal
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Section 100.41: Valuative criterion for the diagonal
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Section 100.42: Valuative criterion for universal closedness
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Section 100.43: Valuative criterion for properness
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Section 100.44: Local complete intersection morphisms
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Section 100.45: Stabilizer preserving morphisms
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Section 100.46: Normalization
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Section 100.47: Points and specializations
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Section 100.48: Decent algebraic stacks
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Section 100.49: Points on decent stacks
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Section 100.50: Integral algebraic stacks
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Section 100.51: Residual gerbes