109 Examples
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Section 109.1: Introduction
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Section 109.2: An empty limit
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Section 109.3: A zero limit
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Section 109.4: Non-quasi-compact inverse limit of quasi-compact spaces
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Section 109.5: The structure sheaf on the fibre product
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Section 109.6: A nonintegral connected scheme whose local rings are domains
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Section 109.7: Noncomplete completion
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Section 109.8: Noncomplete quotient
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Section 109.9: Completion is not exact
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Section 109.10: The category of complete modules is not abelian
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Section 109.11: The category of derived complete modules
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Section 109.12: Nonflat completions
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Section 109.13: Nonabelian category of quasi-coherent modules
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Section 109.14: Regular sequences and base change
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Section 109.15: A Noetherian ring of infinite dimension
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Section 109.16: Local rings with nonreduced completion
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Section 109.17: Another local ring with nonreduced completion
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Section 109.18: A non catenary Noetherian local ring
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Section 109.19: Existence of bad local Noetherian rings
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Section 109.20: Dimension in Noetherian Jacobson rings
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Section 109.21: Underlying space Noetherian not Noetherian
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Section 109.22: Non-quasi-affine variety with quasi-affine normalization
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Section 109.23: Taking scheme theoretic images
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Section 109.24: Images of locally closed subsets
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Section 109.25: A locally closed subscheme which is not open in closed
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Section 109.26: Nonexistence of suitable opens
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Section 109.27: Nonexistence of quasi-compact dense open subscheme
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Section 109.28: Affines over algebraic spaces
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Section 109.29: Pushforward of quasi-coherent modules
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Section 109.30: A nonfinite module with finite free rank 1 stalks
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Section 109.31: A noninvertible ideal invertible in stalks
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Section 109.32: A finite flat module which is not projective
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Section 109.33: A projective module which is not locally free
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Section 109.34: Zero dimensional local ring with nonzero flat ideal
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Section 109.35: An epimorphism of zero-dimensional rings which is not surjective
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Section 109.36: Finite type, not finitely presented, flat at prime
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Section 109.37: Finite type, flat and not of finite presentation
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Section 109.38: Topology of a finite type ring map
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Section 109.39: Pure not universally pure
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Section 109.40: A formally smooth non-flat ring map
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Section 109.41: A formally étale non-flat ring map
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Section 109.42: A formally étale ring map with nontrivial cotangent complex
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Section 109.43: Flat and formally unramified is not formally étale
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Section 109.44: Ideals generated by sets of idempotents and localization
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Section 109.45: A ring map which identifies local rings which is not ind-étale
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Section 109.46: Non flasque quasi-coherent sheaf associated to injective module
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Section 109.47: A non-separated flat group scheme
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Section 109.48: A non-flat group scheme with flat identity component
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Section 109.49: A non-separated group algebraic space over a field
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Section 109.50: Specializations between points in fibre étale morphism
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Section 109.51: A torsor which is not an fppf torsor
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Section 109.52: Stack with quasi-compact flat covering which is not algebraic
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Section 109.53: Limit preserving on objects, not limit preserving
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Section 109.54: A non-algebraic classifying stack
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Section 109.55: Sheaf with quasi-compact flat covering which is not algebraic
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Section 109.56: Sheaves and specializations
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Section 109.57: Sheaves and constructible functions
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Section 109.58: The lisse-étale site is not functorial
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Section 109.59: Sheaves on the category of Noetherian schemes
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Section 109.60: Derived pushforward of quasi-coherent modules
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Section 109.61: A big abelian category
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Section 109.62: Weakly associated points and scheme theoretic density
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Section 109.63: Example of non-additivity of traces
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Section 109.64: Being projective is not local on the base
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Section 109.65: Non-effective descent data for projective schemes
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Section 109.66: A family of curves whose total space is not a scheme
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Section 109.67: Derived base change
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Section 109.68: An interesting compact object
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Section 109.69: Two differential graded categories
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Section 109.70: The stack of proper algebraic spaces is not algebraic
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Section 109.71: An example of a non-algebraic Hom-stack
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Section 109.72: An algebraic stack not satisfying strong formal effectiveness
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Section 109.73: A counter example to Grothendieck's existence theorem
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Section 109.74: Affine formal algebraic spaces
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Section 109.75: Flat maps are not directed limits of finitely presented flat maps
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Section 109.76: The category of modules modulo torsion modules
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Section 109.77: Different colimit topologies
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Section 109.78: Universally submersive but not V covering
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Section 109.79: The spectrum of the integers is not quasi-compact