106 Examples

Section 106.1: Introduction
Section 106.2: An empty limit
Section 106.3: A zero limit
Section 106.4: Non-quasi-compact inverse limit of quasi-compact spaces
- Lemma 106.4.1
Section 106.5: A nonintegral connected scheme whose local rings are domains
Section 106.6: Noncomplete completion
- Equation 106.6.0.1
- Lemma 106.6.1
Section 106.7: Noncomplete quotient
- Lemma 106.7.1
Section 106.8: Completion is not exact
- Lemma 106.8.1 slogan
Section 106.9: The category of complete modules is not abelian
- Lemma 106.9.1
Section 106.10: The category of derived complete modules
- Lemma 106.10.1
Section 106.11: Nonflat completions
- Lemma 106.11.1
- Lemma 106.11.2
- Lemma 106.11.3
- Lemma 106.11.4
- Lemma 106.11.5
- Lemma 106.11.6
  - Equation 106.11.6.1
- Lemma 106.11.7
Section 106.12: Nonabelian category of quasi-coherent modules
- Lemma 106.12.1
Section 106.13: Regular sequences and base change
- Lemma 106.13.1
- Lemma 106.13.2
Section 106.14: A Noetherian ring of infinite dimension
Section 106.15: Local rings with nonreduced completion
Section 106.16: A non catenary Noetherian local ring
Section 106.17: Existence of bad local Noetherian rings
Section 106.18: Dimension in Noetherian Jacobson rings
- Lemma 106.18.1
Section 106.19: Non-quasi-affine variety with quasi-affine normalization
- Lemma 106.19.1
Section 106.20: A locally closed subscheme which is not open in closed
Section 106.21: Nonexistence of suitable opens
- Lemma 106.21.1
- Lemma 106.21.2
Section 106.22: Nonexistence of quasi-compact dense open subscheme
- Lemma 106.22.1
Section 106.23: Affines over algebraic spaces
- Lemma 106.23.1
Section 106.24: Pushforward of quasi-coherent modules
- Lemma 106.24.1
Section 106.25: A nonfinite module with finite free rank 1 stalks
Section 106.26: A noninvertible ideal invertible in stalks
- Lemma 106.26.1
Section 106.27: A finite flat module which is not projective
- Lemma 106.27.1
Section 106.28: A projective module which is not locally free
- Lemma 106.28.1
- Lemma 106.28.2
- Lemma 106.28.3
- Lemma 106.28.4
Section 106.29: Zero dimensional local ring with nonzero flat ideal
- Lemma 106.29.1 slogan
Section 106.30: An epimorphism of zero-dimensional rings which is not surjective
- Lemma 106.30.1
Section 106.31: Finite type, not finitely presented, flat at prime
- Lemma 106.31.1
Section 106.32: Finite type, flat and not of finite presentation
- Lemma 106.32.1
Section 106.33: Topology of a finite type ring map
- Lemma 106.33.1
Section 106.34: Pure not universally pure
- Lemma 106.34.1
Section 106.35: A formally smooth non-flat ring map
- Lemma 106.35.1
Section 106.36: A formally étale non-flat ring map
- Lemma 106.36.1
Section 106.37: A formally étale ring map with nontrivial cotangent complex
- Lemma 106.37.1
Section 106.38: Ideals generated by sets of idempotents and localization
- Lemma 106.38.1
Section 106.39: A ring map which identifies local rings which is not ind-étale
- Lemma 106.39.1
Section 106.40: Non flasque quasi-coherent sheaf associated to injective module
- Lemma 106.40.1
- Lemma 106.40.2
Section 106.41: A non-separated flat group scheme
- Lemma 106.41.1
- Lemma 106.41.2
Section 106.42: A non-flat group scheme with flat identity component
- Lemma 106.42.1
Section 106.43: A non-separated group algebraic space over a field
- Lemma 106.43.1
Section 106.44: Specializations between points in fibre étale morphism
- Lemma 106.44.1
Section 106.45: A torsor which is not an fppf torsor
- Lemma 106.45.1
Section 106.46: Stack with quasi-compact flat covering which is not algebraic
- Lemma 106.46.1
Section 106.47: Limit preserving on objects, not limit preserving
- Lemma 106.47.1
Section 106.48: A non-algebraic classifying stack
Section 106.49: Sheaf with quasi-compact flat covering which is not algebraic
- Lemma 106.49.1
Section 106.50: Sheaves and specializations
- Lemma 106.50.1
- Remark 106.50.2
Section 106.51: Sheaves and constructible functions
- Lemma 106.51.1
Section 106.52: The lisse-étale site is not functorial
- Lemma 106.52.1
Section 106.53: Derived pushforward of quasi-coherent modules
- Lemma 106.53.1
- Lemma 106.53.2
- Lemma 106.53.3
Section 106.54: A big abelian category
- Lemma 106.54.1
Section 106.55: Weakly associated points and scheme theoretic density
- Lemma 106.55.1
Section 106.56: Example of non-additivity of traces
- Equation 106.56.0.1
- Lemma 106.56.1
Section 106.57: Being projective is not local on the base
- Lemma 106.57.1
Section 106.58: Non-effective descent data for projective schemes
- Lemma 106.58.1
Section 106.59: A family of curves whose total space is not a scheme
- Equation 106.59.0.1
- Lemma 106.59.1
Section 106.60: Derived base change
- Lemma 106.60.1
Section 106.61: An interesting compact object
- Lemma 106.61.1
Section 106.62: Two differential graded categories
Section 106.63: The stack of proper algebraic spaces is not algebraic
- Lemma 106.63.1
Section 106.64: An example of a non-algebraic Hom-stack
- Lemma 106.64.1
- Lemma 106.64.2
- Lemma 106.64.3
- Proposition 106.64.4
- Remark 106.64.5
Section 106.65: An algebraic stack not satisfying strong formal effectiveness
- Lemma 106.65.1
Section 106.66: A counter example to Grothendieck's existence theorem
- Lemma 106.66.1
Section 106.67: Affine formal algebraic spaces
- Lemma 106.67.1
- Lemma 106.67.2
- Lemma 106.67.3
Section 106.68: Flat maps are not directed limits of finitely presented flat maps
- Lemma 106.68.1
Section 106.69: The category of modules modulo torsion modules
- Proposition 106.69.1
- Proposition 106.69.2
- Proposition 106.69.3
- Proposition 106.69.4
Section 106.70: Different colimit topologies
- Lemma 106.70.1
Section 106.71: Universally submersive but not V covering
- Lemma 106.71.1
Section 106.72: The spectrum of the integers is not quasi-compact
- Lemma 106.72.1
- Lemma 106.72.2