104 Examples

Section 104.1: Introduction
Section 104.2: An empty limit
Section 104.3: A zero limit
Section 104.4: Non-quasi-compact inverse limit of quasi-compact spaces
- Lemma 104.4.1
Section 104.5: A nonintegral connected scheme whose local rings are domains
Section 104.6: Noncomplete completion
- Equation 104.6.0.1
- Lemma 104.6.1
Section 104.7: Noncomplete quotient
- Lemma 104.7.1
Section 104.8: Completion is not exact
- Lemma 104.8.1 slogan
Section 104.9: The category of complete modules is not abelian
- Lemma 104.9.1
Section 104.10: The category of derived complete modules
- Lemma 104.10.1
Section 104.11: Nonflat completions
- Lemma 104.11.1
- Lemma 104.11.2
- Lemma 104.11.3
- Lemma 104.11.4
- Lemma 104.11.5
- Lemma 104.11.6
  - Equation 104.11.6.1
- Lemma 104.11.7
Section 104.12: Nonabelian category of quasi-coherent modules
- Lemma 104.12.1
Section 104.13: Regular sequences and base change
- Lemma 104.13.1
- Lemma 104.13.2
Section 104.14: A Noetherian ring of infinite dimension
Section 104.15: Local rings with nonreduced completion
Section 104.16: A non catenary Noetherian local ring
Section 104.17: Existence of bad local Noetherian rings
Section 104.18: Dimension in Noetherian Jacobson rings
- Lemma 104.18.1
Section 104.19: Non-quasi-affine variety with quasi-affine normalization
- Lemma 104.19.1
Section 104.20: A locally closed subscheme which is not open in closed
Section 104.21: Nonexistence of suitable opens
- Lemma 104.21.1
- Lemma 104.21.2
Section 104.22: Nonexistence of quasi-compact dense open subscheme
- Lemma 104.22.1
Section 104.23: Affines over algebraic spaces
- Lemma 104.23.1
Section 104.24: Pushforward of quasi-coherent modules
- Lemma 104.24.1
Section 104.25: A nonfinite module with finite free rank 1 stalks
Section 104.26: A noninvertible ideal invertible in stalks
- Lemma 104.26.1
Section 104.27: A finite flat module which is not projective
- Lemma 104.27.1
Section 104.28: A projective module which is not locally free
- Lemma 104.28.1
- Lemma 104.28.2 slogan
- Lemma 104.28.3
- Lemma 104.28.4
- Lemma 104.28.5
Section 104.29: Zero dimensional local ring with nonzero flat ideal
- Lemma 104.29.1 slogan
Section 104.30: An epimorphism of zero-dimensional rings which is not surjective
- Lemma 104.30.1
Section 104.31: Finite type, not finitely presented, flat at prime
- Lemma 104.31.1
Section 104.32: Finite type, flat and not of finite presentation
- Lemma 104.32.1
Section 104.33: Topology of a finite type ring map
- Lemma 104.33.1
Section 104.34: Pure not universally pure
- Lemma 104.34.1
Section 104.35: A formally smooth non-flat ring map
- Lemma 104.35.1
Section 104.36: A formally étale non-flat ring map
- Lemma 104.36.1
Section 104.37: A formally étale ring map with nontrivial cotangent complex
- Lemma 104.37.1
Section 104.38: Ideals generated by sets of idempotents and localization
- Lemma 104.38.1
Section 104.39: A ring map which identifies local rings which is not ind-étale
- Lemma 104.39.1
Section 104.40: Non flasque quasi-coherent sheaf associated to injective module
- Lemma 104.40.1
- Lemma 104.40.2
Section 104.41: A non-separated flat group scheme
- Lemma 104.41.1
- Lemma 104.41.2
Section 104.42: A non-flat group scheme with flat identity component
- Lemma 104.42.1
Section 104.43: A non-separated group algebraic space over a field
- Lemma 104.43.1
Section 104.44: Specializations between points in fibre étale morphism
- Lemma 104.44.1
Section 104.45: A torsor which is not an fppf torsor
- Lemma 104.45.1
Section 104.46: Stack with quasi-compact flat covering which is not algebraic
- Lemma 104.46.1
Section 104.47: Limit preserving on objects, not limit preserving
- Lemma 104.47.1
Section 104.48: A non-algebraic classifying stack
Section 104.49: Sheaf with quasi-compact flat covering which is not algebraic
- Lemma 104.49.1
Section 104.50: Sheaves and specializations
- Lemma 104.50.1
- Remark 104.50.2
Section 104.51: Sheaves and constructible functions
- Lemma 104.51.1
Section 104.52: The lisse-étale site is not functorial
- Lemma 104.52.1
Section 104.53: Derived pushforward of quasi-coherent modules
- Lemma 104.53.1
- Lemma 104.53.2
- Lemma 104.53.3
Section 104.54: A big abelian category
- Lemma 104.54.1
Section 104.55: Weakly associated points and scheme theoretic density
- Lemma 104.55.1
Section 104.56: Example of non-additivity of traces
- Equation 104.56.0.1
- Lemma 104.56.1
Section 104.57: Being projective is not local on the base
- Lemma 104.57.1
Section 104.58: Descent data for schemes need not be effective, even for a projective morphism
- Lemma 104.58.1
Section 104.59: A family of curves whose total space is not a scheme
- Equation 104.59.0.1
- Lemma 104.59.1
Section 104.60: Derived base change
- Lemma 104.60.1
Section 104.61: An interesting compact object
- Lemma 104.61.1
Section 104.62: Two differential graded categories
Section 104.63: The stack of proper algebraic spaces is not algebraic
- Lemma 104.63.1
Section 104.64: An example of a non-algebraic Hom-stack
- Lemma 104.64.1
- Lemma 104.64.2
- Lemma 104.64.3
- Proposition 104.64.4
- Remark 104.64.5
Section 104.65: An algebraic stack not satisfying strong formal effectiveness
- Lemma 104.65.1
Section 104.66: A counter example to Grothendieck's existence theorem
- Lemma 104.66.1
Section 104.67: Affine formal algebraic spaces
- Lemma 104.67.1
- Lemma 104.67.2
- Lemma 104.67.3
Section 104.68: Flat maps are not directed limits of finitely presented flat maps
- Lemma 104.68.1
Section 104.69: The category of modules modulo torsion modules
- Proposition 104.69.1
- Proposition 104.69.2
- Proposition 104.69.3
- Proposition 104.69.4
Section 104.70: Different colimit topologies
- Lemma 104.70.1
Section 104.71: Universally submersive but not V covering
- Lemma 104.71.1
Section 104.72: The spectrum of the integers is not quasi-compact
- Lemma 104.72.1
- Lemma 104.72.2