110 Examples

Section 110.1: Introduction
Section 110.2: An empty limit
Section 110.3: A zero limit
Section 110.4: Non-quasi-compact inverse limit of quasi-compact spaces
- Lemma 110.4.1
Section 110.5: The structure sheaf on the fibre product
Section 110.6: A nonintegral connected scheme whose local rings are domains
Section 110.7: Noncomplete completion
- Equation 110.7.0.1
- Lemma 110.7.1
Section 110.8: Noncomplete quotient
- Lemma 110.8.1
Section 110.9: Completion is not exact
- Lemma 110.9.1 slogan
Section 110.10: The category of complete modules is not abelian
- Lemma 110.10.1
Section 110.11: The category of derived complete modules
- Lemma 110.11.1
Section 110.12: Nonflat completions
- Lemma 110.12.1
- Lemma 110.12.2
- Lemma 110.12.3
- Lemma 110.12.4
- Lemma 110.12.5
- Lemma 110.12.6
  - Equation 110.12.6.1
- Lemma 110.12.7
Section 110.13: Nonabelian category of quasi-coherent modules
- Lemma 110.13.1
Section 110.14: Nonsplit locally split sequence
- Lemma 110.14.1
Section 110.15: Regular sequences and base change
- Lemma 110.15.1
- Lemma 110.15.2
Section 110.16: A Noetherian ring of infinite dimension
Section 110.17: Local rings with nonreduced completion
Section 110.18: Another local ring with nonreduced completion
- Lemma 110.18.1
Section 110.19: A non catenary Noetherian local ring
Section 110.20: Existence of bad local Noetherian rings
Section 110.21: Dimension in Noetherian Jacobson rings
- Lemma 110.21.1
Section 110.22: Underlying space Noetherian not Noetherian
- Example 110.22.1
- Example 110.22.2
Section 110.23: Non-quasi-affine variety with quasi-affine normalization
- Lemma 110.23.1
Section 110.24: Taking scheme theoretic images
Section 110.25: Images of locally closed subsets
- Lemma 110.25.1
Section 110.26: A locally closed subscheme which is not open in closed
Section 110.27: Nonexistence of suitable opens
- Lemma 110.27.1
- Lemma 110.27.2
Section 110.28: Nonexistence of quasi-compact dense open subscheme
- Lemma 110.28.1
Section 110.29: Affines over algebraic spaces
- Lemma 110.29.1
Section 110.30: Pushforward of quasi-coherent modules
- Lemma 110.30.1
Section 110.31: A nonfinite module with finite free rank 1 stalks
Section 110.32: A noninvertible ideal invertible in stalks
- Lemma 110.32.1
Section 110.33: A finite flat module which is not projective
- Lemma 110.33.1
Section 110.34: A projective module which is not locally free
- Lemma 110.34.1
- Lemma 110.34.2
- Lemma 110.34.3
- Lemma 110.34.4
Section 110.35: Zero dimensional local ring with nonzero flat ideal
- Lemma 110.35.1 slogan
Section 110.36: An epimorphism of zero-dimensional rings which is not surjective
- Lemma 110.36.1
Section 110.37: Finite type, not finitely presented, flat at prime
- Lemma 110.37.1
Section 110.38: Finite type, flat and not of finite presentation
- Lemma 110.38.1
Section 110.39: Topology of a finite type ring map
- Lemma 110.39.1
Section 110.40: Pure not universally pure
- Lemma 110.40.1
Section 110.41: A formally smooth non-flat ring map
- Lemma 110.41.1
Section 110.42: A formally étale non-flat ring map
- Lemma 110.42.1
Section 110.43: A formally étale ring map with nontrivial cotangent complex
- Lemma 110.43.1
Section 110.44: Flat and formally unramified is not formally étale
- Lemma 110.44.1
- Lemma 110.44.2
- Remark 110.44.3
- Lemma 110.44.4
Section 110.45: Ideals generated by sets of idempotents and localization
- Lemma 110.45.1
Section 110.46: A ring map which identifies local rings which is not ind-étale
- Lemma 110.46.1
Section 110.47: Non flasque quasi-coherent sheaf associated to injective module
- Lemma 110.47.1
- Lemma 110.47.2
Section 110.48: A non-separated flat group scheme
- Lemma 110.48.1
- Lemma 110.48.2
Section 110.49: A non-flat group scheme with flat identity component
- Lemma 110.49.1
Section 110.50: A non-separated group algebraic space over a field
- Lemma 110.50.1
Section 110.51: Specializations between points in fibre étale morphism
- Lemma 110.51.1
Section 110.52: A torsor which is not an fppf torsor
- Lemma 110.52.1
Section 110.53: Stack with quasi-compact flat covering which is not algebraic
- Lemma 110.53.1
Section 110.54: Limit preserving on objects, not limit preserving
- Lemma 110.54.1
Section 110.55: A non-algebraic classifying stack
Section 110.56: Sheaf with quasi-compact flat covering which is not algebraic
- Lemma 110.56.1
Section 110.57: Sheaves and specializations
- Lemma 110.57.1
- Remark 110.57.2
Section 110.58: Sheaves and constructible functions
- Lemma 110.58.1
Section 110.59: The lisse-étale site is not functorial
- Lemma 110.59.1
Section 110.60: Sheaves on the category of Noetherian schemes
- Lemma 110.60.1
Section 110.61: Derived pushforward of quasi-coherent modules
- Lemma 110.61.1
- Lemma 110.61.2
- Lemma 110.61.3
Section 110.62: A big abelian category
- Lemma 110.62.1
Section 110.63: Weakly associated points and scheme theoretic density
- Lemma 110.63.1
Section 110.64: Example of non-additivity of traces
- Equation 110.64.0.1
- Lemma 110.64.1
Section 110.65: Being projective is not local on the base
- Lemma 110.65.1
Section 110.66: Non-effective descent data for projective schemes
- Lemma 110.66.1
Section 110.67: A family of curves whose total space is not a scheme
- Equation 110.67.0.1
- Lemma 110.67.1
Section 110.68: Derived base change
- Lemma 110.68.1
Section 110.69: An interesting compact object
- Lemma 110.69.1
Section 110.70: Two differential graded categories
Section 110.71: The stack of proper algebraic spaces is not algebraic
- Lemma 110.71.1
Section 110.72: An example of a non-algebraic Hom-stack
- Lemma 110.72.1
- Lemma 110.72.2
- Lemma 110.72.3
- Proposition 110.72.4
- Remark 110.72.5
Section 110.73: An algebraic stack not satisfying strong formal effectiveness
- Lemma 110.73.1
Section 110.74: A counter example to Grothendieck's existence theorem
- Lemma 110.74.1
Section 110.75: Affine formal algebraic spaces
- Lemma 110.75.1
- Lemma 110.75.2
- Lemma 110.75.3
Section 110.76: Flat maps are not directed limits of finitely presented flat maps
- Lemma 110.76.1
Section 110.77: The category of modules modulo torsion modules
- Proposition 110.77.1
- Proposition 110.77.2
- Proposition 110.77.3
- Proposition 110.77.4
Section 110.78: Different colimit topologies
- Lemma 110.78.1
Section 110.79: Universally submersive but not V covering
- Lemma 110.79.1
Section 110.80: The spectrum of the integers is not quasi-compact
- Lemma 110.80.1
- Lemma 110.80.2