\begin{equation*}
\DeclareMathOperator\Coim{Coim}
\DeclareMathOperator\Coker{Coker}
\DeclareMathOperator\Ext{Ext}
\DeclareMathOperator\Hom{Hom}
\DeclareMathOperator\Im{Im}
\DeclareMathOperator\Ker{Ker}
\DeclareMathOperator\Mor{Mor}
\DeclareMathOperator\Ob{Ob}
\DeclareMathOperator\Sh{Sh}
\DeclareMathOperator\SheafExt{\mathcal{E}\mathit{xt}}
\DeclareMathOperator\SheafHom{\mathcal{H}\mathit{om}}
\DeclareMathOperator\Spec{Spec}
\newcommand\colim{\mathop{\mathrm{colim}}\nolimits}
\newcommand\lim{\mathop{\mathrm{lim}}\nolimits}
\newcommand\Qcoh{\mathit{Qcoh}}
\newcommand\Sch{\mathit{Sch}}
\newcommand\QCohstack{\mathcal{QC}\!\mathit{oh}}
\newcommand\Cohstack{\mathcal{C}\!\mathit{oh}}
\newcommand\Spacesstack{\mathcal{S}\!\mathit{paces}}
\newcommand\Quotfunctor{\mathrm{Quot}}
\newcommand\Hilbfunctor{\mathrm{Hilb}}
\newcommand\Curvesstack{\mathcal{C}\!\mathit{urves}}
\newcommand\Polarizedstack{\mathcal{P}\!\mathit{olarized}}
\newcommand\Complexesstack{\mathcal{C}\!\mathit{omplexes}}
\newcommand\Pic{\mathop{\mathrm{Pic}}\nolimits}
\newcommand\Picardstack{\mathcal{P}\!\mathit{ic}}
\newcommand\Picardfunctor{\mathrm{Pic}}
\newcommand\Deformationcategory{\mathcal{D}\!\mathit{ef}}
\end{equation*}
102 Examples
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Section 102.1: Introduction
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Section 102.2: An empty limit
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Section 102.3: A zero limit
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Section 102.4: Non-quasi-compact inverse limit of quasi-compact spaces
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Section 102.5: A nonintegral connected scheme whose local rings are domains
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Section 102.6: Noncomplete completion
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Section 102.7: Noncomplete quotient
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Section 102.8: Completion is not exact
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Section 102.9: The category of complete modules is not abelian
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Section 102.10: The category of derived complete modules
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Section 102.11: Nonflat completions
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Section 102.12: Nonabelian category of quasi-coherent modules
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Section 102.13: Regular sequences and base change
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Section 102.14: A Noetherian ring of infinite dimension
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Section 102.15: Local rings with nonreduced completion
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Section 102.16: A non catenary Noetherian local ring
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Section 102.17: Existence of bad local Noetherian rings
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Section 102.18: Dimension in Noetherian Jacobson rings
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Section 102.19: Non-quasi-affine variety with quasi-affine normalization
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Section 102.20: A locally closed subscheme which is not open in closed
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Section 102.21: Nonexistence of suitable opens
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Section 102.22: Nonexistence of quasi-compact dense open subscheme
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Section 102.23: Affines over algebraic spaces
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Section 102.24: Pushforward of quasi-coherent modules
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Section 102.25: A nonfinite module with finite free rank 1 stalks
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Section 102.26: A noninvertible ideal invertible in stalks
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Section 102.27: A finite flat module which is not projective
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Section 102.28: A projective module which is not locally free
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Section 102.29: Zero dimensional local ring with nonzero flat ideal
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Section 102.30: An epimorphism of zero-dimensional rings which is not surjective
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Section 102.31: Finite type, not finitely presented, flat at prime
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Section 102.32: Finite type, flat and not of finite presentation
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Section 102.33: Topology of a finite type ring map
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Section 102.34: Pure not universally pure
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Section 102.35: A formally smooth non-flat ring map
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Section 102.36: A formally étale non-flat ring map
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Section 102.37: A formally étale ring map with nontrivial cotangent complex
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Section 102.38: Ideals generated by sets of idempotents and localization
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Section 102.39: A ring map which identifies local rings which is not ind-étale
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Section 102.40: Non flasque quasi-coherent sheaf associated to injective module
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Section 102.41: A non-separated flat group scheme
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Section 102.42: A non-flat group scheme with flat identity component
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Section 102.43: A non-separated group algebraic space over a field
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Section 102.44: Specializations between points in fibre étale morphism
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Section 102.45: A torsor which is not an fppf torsor
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Section 102.46: Stack with quasi-compact flat covering which is not algebraic
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Section 102.47: Limit preserving on objects, not limit preserving
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Section 102.48: A non-algebraic classifying stack
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Section 102.49: Sheaf with quasi-compact flat covering which is not algebraic
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Section 102.50: Sheaves and specializations
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Section 102.51: Sheaves and constructible functions
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Section 102.52: The lisse-étale site is not functorial
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Section 102.53: Derived pushforward of quasi-coherent modules
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Section 102.54: A big abelian category
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Section 102.55: Weakly associated points and scheme theoretic density
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Section 102.56: Example of non-additivity of traces
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Section 102.57: Being projective is not local on the base
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Section 102.58: Descent data for schemes need not be effective, even for a projective morphism
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Section 102.59: A family of curves whose total space is not a scheme
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Section 102.60: Derived base change
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Section 102.61: An interesting compact object
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Section 102.62: Two differential graded categories
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Section 102.63: The stack of proper algebraic spaces is not algebraic
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Section 102.64: An example of a non-algebraic Hom-stack
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Section 102.65: An algebraic stack not satisfying strong formal effectiveness
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Section 102.66: A counter example to Grothendieck's existence theorem
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Section 102.67: Affine formal algebraic spaces
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Section 102.68: Flat maps are not directed limits of finitely presented flat maps
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Section 102.69: The category of modules modulo torsion modules
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Section 102.70: Different colimit topologies
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Section 102.71: Universally submersive but not V covering
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Section 102.72: The spectrum of the integers is not quasi-compact