108 Examples

Section 108.1: Introduction
Section 108.2: An empty limit
Section 108.3: A zero limit
Section 108.4: Non-quasi-compact inverse limit of quasi-compact spaces
- Lemma 108.4.1
Section 108.5: The structure sheaf on the fibre product
Section 108.6: A nonintegral connected scheme whose local rings are domains
Section 108.7: Noncomplete completion
- Equation 108.7.0.1
- Lemma 108.7.1
Section 108.8: Noncomplete quotient
- Lemma 108.8.1
Section 108.9: Completion is not exact
- Lemma 108.9.1 slogan
Section 108.10: The category of complete modules is not abelian
- Lemma 108.10.1
Section 108.11: The category of derived complete modules
- Lemma 108.11.1
Section 108.12: Nonflat completions
- Lemma 108.12.1
- Lemma 108.12.2
- Lemma 108.12.3
- Lemma 108.12.4
- Lemma 108.12.5
- Lemma 108.12.6
  - Equation 108.12.6.1
- Lemma 108.12.7
Section 108.13: Nonabelian category of quasi-coherent modules
- Lemma 108.13.1
Section 108.14: Regular sequences and base change
- Lemma 108.14.1
- Lemma 108.14.2
Section 108.15: A Noetherian ring of infinite dimension
Section 108.16: Local rings with nonreduced completion
Section 108.17: Another local ring with nonreduced completion
- Lemma 108.17.1
Section 108.18: A non catenary Noetherian local ring
Section 108.19: Existence of bad local Noetherian rings
Section 108.20: Dimension in Noetherian Jacobson rings
- Lemma 108.20.1
Section 108.21: Underlying space Noetherian not Noetherian
- Example 108.21.1
- Example 108.21.2
Section 108.22: Non-quasi-affine variety with quasi-affine normalization
- Lemma 108.22.1
Section 108.23: Taking scheme theoretic images
Section 108.24: A locally closed subscheme which is not open in closed
Section 108.25: Nonexistence of suitable opens
- Lemma 108.25.1
- Lemma 108.25.2
Section 108.26: Nonexistence of quasi-compact dense open subscheme
- Lemma 108.26.1
Section 108.27: Affines over algebraic spaces
- Lemma 108.27.1
Section 108.28: Pushforward of quasi-coherent modules
- Lemma 108.28.1
Section 108.29: A nonfinite module with finite free rank 1 stalks
Section 108.30: A noninvertible ideal invertible in stalks
- Lemma 108.30.1
Section 108.31: A finite flat module which is not projective
- Lemma 108.31.1
Section 108.32: A projective module which is not locally free
- Lemma 108.32.1
- Lemma 108.32.2
- Lemma 108.32.3
- Lemma 108.32.4
Section 108.33: Zero dimensional local ring with nonzero flat ideal
- Lemma 108.33.1 slogan
Section 108.34: An epimorphism of zero-dimensional rings which is not surjective
- Lemma 108.34.1
Section 108.35: Finite type, not finitely presented, flat at prime
- Lemma 108.35.1
Section 108.36: Finite type, flat and not of finite presentation
- Lemma 108.36.1
Section 108.37: Topology of a finite type ring map
- Lemma 108.37.1
Section 108.38: Pure not universally pure
- Lemma 108.38.1
Section 108.39: A formally smooth non-flat ring map
- Lemma 108.39.1
Section 108.40: A formally étale non-flat ring map
- Lemma 108.40.1
Section 108.41: A formally étale ring map with nontrivial cotangent complex
- Lemma 108.41.1
Section 108.42: Flat and formally unramified is not formally étale
- Lemma 108.42.1
- Lemma 108.42.2
- Remark 108.42.3
- Lemma 108.42.4
Section 108.43: Ideals generated by sets of idempotents and localization
- Lemma 108.43.1
Section 108.44: A ring map which identifies local rings which is not ind-étale
- Lemma 108.44.1
Section 108.45: Non flasque quasi-coherent sheaf associated to injective module
- Lemma 108.45.1
- Lemma 108.45.2
Section 108.46: A non-separated flat group scheme
- Lemma 108.46.1
- Lemma 108.46.2
Section 108.47: A non-flat group scheme with flat identity component
- Lemma 108.47.1
Section 108.48: A non-separated group algebraic space over a field
- Lemma 108.48.1
Section 108.49: Specializations between points in fibre étale morphism
- Lemma 108.49.1
Section 108.50: A torsor which is not an fppf torsor
- Lemma 108.50.1
Section 108.51: Stack with quasi-compact flat covering which is not algebraic
- Lemma 108.51.1
Section 108.52: Limit preserving on objects, not limit preserving
- Lemma 108.52.1
Section 108.53: A non-algebraic classifying stack
Section 108.54: Sheaf with quasi-compact flat covering which is not algebraic
- Lemma 108.54.1
Section 108.55: Sheaves and specializations
- Lemma 108.55.1
- Remark 108.55.2
Section 108.56: Sheaves and constructible functions
- Lemma 108.56.1
Section 108.57: The lisse-étale site is not functorial
- Lemma 108.57.1
Section 108.58: Sheaves on the category of Noetherian schemes
- Lemma 108.58.1
Section 108.59: Derived pushforward of quasi-coherent modules
- Lemma 108.59.1
- Lemma 108.59.2
- Lemma 108.59.3
Section 108.60: A big abelian category
- Lemma 108.60.1
Section 108.61: Weakly associated points and scheme theoretic density
- Lemma 108.61.1
Section 108.62: Example of non-additivity of traces
- Equation 108.62.0.1
- Lemma 108.62.1
Section 108.63: Being projective is not local on the base
- Lemma 108.63.1
Section 108.64: Non-effective descent data for projective schemes
- Lemma 108.64.1
Section 108.65: A family of curves whose total space is not a scheme
- Equation 108.65.0.1
- Lemma 108.65.1
Section 108.66: Derived base change
- Lemma 108.66.1
Section 108.67: An interesting compact object
- Lemma 108.67.1
Section 108.68: Two differential graded categories
Section 108.69: The stack of proper algebraic spaces is not algebraic
- Lemma 108.69.1
Section 108.70: An example of a non-algebraic Hom-stack
- Lemma 108.70.1
- Lemma 108.70.2
- Lemma 108.70.3
- Proposition 108.70.4
- Remark 108.70.5
Section 108.71: An algebraic stack not satisfying strong formal effectiveness
- Lemma 108.71.1
Section 108.72: A counter example to Grothendieck's existence theorem
- Lemma 108.72.1
Section 108.73: Affine formal algebraic spaces
- Lemma 108.73.1
- Lemma 108.73.2
- Lemma 108.73.3
Section 108.74: Flat maps are not directed limits of finitely presented flat maps
- Lemma 108.74.1
Section 108.75: The category of modules modulo torsion modules
- Proposition 108.75.1
- Proposition 108.75.2
- Proposition 108.75.3
- Proposition 108.75.4
Section 108.76: Different colimit topologies
- Lemma 108.76.1
Section 108.77: Universally submersive but not V covering
- Lemma 108.77.1
Section 108.78: The spectrum of the integers is not quasi-compact
- Lemma 108.78.1
- Lemma 108.78.2