110 Examples
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Section 110.1: Introduction
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Section 110.2: An empty limit
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Section 110.3: A zero limit
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Section 110.4: Non-quasi-compact inverse limit of quasi-compact spaces
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Section 110.5: The structure sheaf on the fibre product
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Section 110.6: A nonintegral connected scheme whose local rings are domains
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Section 110.7: Noncomplete completion
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Section 110.8: Noncomplete quotient
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Section 110.9: Completion is not exact
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Section 110.10: The category of complete modules is not abelian
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Section 110.11: The category of derived complete modules
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Section 110.12: Nonflat completions
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Section 110.13: Nonabelian category of quasi-coherent modules
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Section 110.14: Regular sequences and base change
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Section 110.15: A Noetherian ring of infinite dimension
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Section 110.16: Local rings with nonreduced completion
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Section 110.17: Another local ring with nonreduced completion
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Section 110.18: A non catenary Noetherian local ring
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Section 110.19: Existence of bad local Noetherian rings
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Section 110.20: Dimension in Noetherian Jacobson rings
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Section 110.21: Underlying space Noetherian not Noetherian
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Section 110.22: Non-quasi-affine variety with quasi-affine normalization
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Section 110.23: Taking scheme theoretic images
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Section 110.24: Images of locally closed subsets
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Section 110.25: A locally closed subscheme which is not open in closed
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Section 110.26: Nonexistence of suitable opens
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Section 110.27: Nonexistence of quasi-compact dense open subscheme
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Section 110.28: Affines over algebraic spaces
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Section 110.29: Pushforward of quasi-coherent modules
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Section 110.30: A nonfinite module with finite free rank 1 stalks
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Section 110.31: A noninvertible ideal invertible in stalks
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Section 110.32: A finite flat module which is not projective
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Section 110.33: A projective module which is not locally free
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Section 110.34: Zero dimensional local ring with nonzero flat ideal
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Section 110.35: An epimorphism of zero-dimensional rings which is not surjective
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Section 110.36: Finite type, not finitely presented, flat at prime
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Section 110.37: Finite type, flat and not of finite presentation
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Section 110.38: Topology of a finite type ring map
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Section 110.39: Pure not universally pure
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Section 110.40: A formally smooth non-flat ring map
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Section 110.41: A formally étale non-flat ring map
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Section 110.42: A formally étale ring map with nontrivial cotangent complex
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Section 110.43: Flat and formally unramified is not formally étale
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Section 110.44: Ideals generated by sets of idempotents and localization
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Section 110.45: A ring map which identifies local rings which is not ind-étale
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Section 110.46: Non flasque quasi-coherent sheaf associated to injective module
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Section 110.47: A non-separated flat group scheme
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Section 110.48: A non-flat group scheme with flat identity component
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Section 110.49: A non-separated group algebraic space over a field
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Section 110.50: Specializations between points in fibre étale morphism
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Section 110.51: A torsor which is not an fppf torsor
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Section 110.52: Stack with quasi-compact flat covering which is not algebraic
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Section 110.53: Limit preserving on objects, not limit preserving
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Section 110.54: A non-algebraic classifying stack
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Section 110.55: Sheaf with quasi-compact flat covering which is not algebraic
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Section 110.56: Sheaves and specializations
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Section 110.57: Sheaves and constructible functions
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Section 110.58: The lisse-étale site is not functorial
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Section 110.59: Sheaves on the category of Noetherian schemes
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Section 110.60: Derived pushforward of quasi-coherent modules
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Section 110.61: A big abelian category
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Section 110.62: Weakly associated points and scheme theoretic density
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Section 110.63: Example of non-additivity of traces
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Section 110.64: Being projective is not local on the base
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Section 110.65: Non-effective descent data for projective schemes
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Section 110.66: A family of curves whose total space is not a scheme
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Section 110.67: Derived base change
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Section 110.68: An interesting compact object
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Section 110.69: Two differential graded categories
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Section 110.70: The stack of proper algebraic spaces is not algebraic
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Section 110.71: An example of a non-algebraic Hom-stack
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Section 110.72: An algebraic stack not satisfying strong formal effectiveness
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Section 110.73: A counter example to Grothendieck's existence theorem
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Section 110.74: Affine formal algebraic spaces
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Section 110.75: Flat maps are not directed limits of finitely presented flat maps
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Section 110.76: The category of modules modulo torsion modules
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Section 110.77: Different colimit topologies
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Section 110.78: Universally submersive but not V covering
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Section 110.79: The spectrum of the integers is not quasi-compact