107 Examples

Section 107.1: Introduction
Section 107.2: An empty limit
Section 107.3: A zero limit
Section 107.4: Non-quasi-compact inverse limit of quasi-compact spaces
- Lemma 107.4.1
Section 107.5: A nonintegral connected scheme whose local rings are domains
Section 107.6: Noncomplete completion
- Equation 107.6.0.1
- Lemma 107.6.1
Section 107.7: Noncomplete quotient
- Lemma 107.7.1
Section 107.8: Completion is not exact
- Lemma 107.8.1 slogan
Section 107.9: The category of complete modules is not abelian
- Lemma 107.9.1
Section 107.10: The category of derived complete modules
- Lemma 107.10.1
Section 107.11: Nonflat completions
- Lemma 107.11.1
- Lemma 107.11.2
- Lemma 107.11.3
- Lemma 107.11.4
- Lemma 107.11.5
- Lemma 107.11.6
  - Equation 107.11.6.1
- Lemma 107.11.7
Section 107.12: Nonabelian category of quasi-coherent modules
- Lemma 107.12.1
Section 107.13: Regular sequences and base change
- Lemma 107.13.1
- Lemma 107.13.2
Section 107.14: A Noetherian ring of infinite dimension
Section 107.15: Local rings with nonreduced completion
Section 107.16: A non catenary Noetherian local ring
Section 107.17: Existence of bad local Noetherian rings
Section 107.18: Dimension in Noetherian Jacobson rings
- Lemma 107.18.1
Section 107.19: Non-quasi-affine variety with quasi-affine normalization
- Lemma 107.19.1
Section 107.20: A locally closed subscheme which is not open in closed
Section 107.21: Nonexistence of suitable opens
- Lemma 107.21.1
- Lemma 107.21.2
Section 107.22: Nonexistence of quasi-compact dense open subscheme
- Lemma 107.22.1
Section 107.23: Affines over algebraic spaces
- Lemma 107.23.1
Section 107.24: Pushforward of quasi-coherent modules
- Lemma 107.24.1
Section 107.25: A nonfinite module with finite free rank 1 stalks
Section 107.26: A noninvertible ideal invertible in stalks
- Lemma 107.26.1
Section 107.27: A finite flat module which is not projective
- Lemma 107.27.1
Section 107.28: A projective module which is not locally free
- Lemma 107.28.1
- Lemma 107.28.2
- Lemma 107.28.3
- Lemma 107.28.4
Section 107.29: Zero dimensional local ring with nonzero flat ideal
- Lemma 107.29.1 slogan
Section 107.30: An epimorphism of zero-dimensional rings which is not surjective
- Lemma 107.30.1
Section 107.31: Finite type, not finitely presented, flat at prime
- Lemma 107.31.1
Section 107.32: Finite type, flat and not of finite presentation
- Lemma 107.32.1
Section 107.33: Topology of a finite type ring map
- Lemma 107.33.1
Section 107.34: Pure not universally pure
- Lemma 107.34.1
Section 107.35: A formally smooth non-flat ring map
- Lemma 107.35.1
Section 107.36: A formally étale non-flat ring map
- Lemma 107.36.1
Section 107.37: A formally étale ring map with nontrivial cotangent complex
- Lemma 107.37.1
Section 107.38: Ideals generated by sets of idempotents and localization
- Lemma 107.38.1
Section 107.39: A ring map which identifies local rings which is not ind-étale
- Lemma 107.39.1
Section 107.40: Non flasque quasi-coherent sheaf associated to injective module
- Lemma 107.40.1
- Lemma 107.40.2
Section 107.41: A non-separated flat group scheme
- Lemma 107.41.1
- Lemma 107.41.2
Section 107.42: A non-flat group scheme with flat identity component
- Lemma 107.42.1
Section 107.43: A non-separated group algebraic space over a field
- Lemma 107.43.1
Section 107.44: Specializations between points in fibre étale morphism
- Lemma 107.44.1
Section 107.45: A torsor which is not an fppf torsor
- Lemma 107.45.1
Section 107.46: Stack with quasi-compact flat covering which is not algebraic
- Lemma 107.46.1
Section 107.47: Limit preserving on objects, not limit preserving
- Lemma 107.47.1
Section 107.48: A non-algebraic classifying stack
Section 107.49: Sheaf with quasi-compact flat covering which is not algebraic
- Lemma 107.49.1
Section 107.50: Sheaves and specializations
- Lemma 107.50.1
- Remark 107.50.2
Section 107.51: Sheaves and constructible functions
- Lemma 107.51.1
Section 107.52: The lisse-étale site is not functorial
- Lemma 107.52.1
Section 107.53: Derived pushforward of quasi-coherent modules
- Lemma 107.53.1
- Lemma 107.53.2
- Lemma 107.53.3
Section 107.54: A big abelian category
- Lemma 107.54.1
Section 107.55: Weakly associated points and scheme theoretic density
- Lemma 107.55.1
Section 107.56: Example of non-additivity of traces
- Equation 107.56.0.1
- Lemma 107.56.1
Section 107.57: Being projective is not local on the base
- Lemma 107.57.1
Section 107.58: Non-effective descent data for projective schemes
- Lemma 107.58.1
Section 107.59: A family of curves whose total space is not a scheme
- Equation 107.59.0.1
- Lemma 107.59.1
Section 107.60: Derived base change
- Lemma 107.60.1
Section 107.61: An interesting compact object
- Lemma 107.61.1
Section 107.62: Two differential graded categories
Section 107.63: The stack of proper algebraic spaces is not algebraic
- Lemma 107.63.1
Section 107.64: An example of a non-algebraic Hom-stack
- Lemma 107.64.1
- Lemma 107.64.2
- Lemma 107.64.3
- Proposition 107.64.4
- Remark 107.64.5
Section 107.65: An algebraic stack not satisfying strong formal effectiveness
- Lemma 107.65.1
Section 107.66: A counter example to Grothendieck's existence theorem
- Lemma 107.66.1
Section 107.67: Affine formal algebraic spaces
- Lemma 107.67.1
- Lemma 107.67.2
- Lemma 107.67.3
Section 107.68: Flat maps are not directed limits of finitely presented flat maps
- Lemma 107.68.1
Section 107.69: The category of modules modulo torsion modules
- Proposition 107.69.1
- Proposition 107.69.2
- Proposition 107.69.3
- Proposition 107.69.4
Section 107.70: Different colimit topologies
- Lemma 107.70.1
Section 107.71: Universally submersive but not V covering
- Lemma 107.71.1
Section 107.72: The spectrum of the integers is not quasi-compact
- Lemma 107.72.1
- Lemma 107.72.2