104 Examples

Section 104.1: Introduction

Section 104.2: An empty limit

Section 104.3: A zero limit

Section 104.4: Nonquasicompact inverse limit of quasicompact spaces

Section 104.5: A nonintegral connected scheme whose local rings are domains

Section 104.6: Noncomplete completion

Section 104.7: Noncomplete quotient

Section 104.8: Completion is not exact

Section 104.9: The category of complete modules is not abelian

Section 104.10: The category of derived complete modules

Section 104.11: Nonflat completions

Section 104.12: Nonabelian category of quasicoherent modules

Section 104.13: Regular sequences and base change

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

Section 104.19: Nonquasiaffine variety with quasiaffine normalization

Section 104.20: A locally closed subscheme which is not open in closed

Section 104.21: Nonexistence of suitable opens

Section 104.22: Nonexistence of quasicompact dense open subscheme

Section 104.23: Affines over algebraic spaces

Section 104.24: Pushforward of quasicoherent modules

Section 104.25: A nonfinite module with finite free rank 1 stalks

Section 104.26: A noninvertible ideal invertible in stalks

Section 104.27: A finite flat module which is not projective

Section 104.28: A projective module which is not locally free

Section 104.29: Zero dimensional local ring with nonzero flat ideal

Section 104.30: An epimorphism of zerodimensional rings which is not surjective

Section 104.31: Finite type, not finitely presented, flat at prime

Section 104.32: Finite type, flat and not of finite presentation

Section 104.33: Topology of a finite type ring map

Section 104.34: Pure not universally pure

Section 104.35: A formally smooth nonflat ring map

Section 104.36: A formally étale nonflat ring map

Section 104.37: A formally étale ring map with nontrivial cotangent complex

Section 104.38: Ideals generated by sets of idempotents and localization

Section 104.39: A ring map which identifies local rings which is not indétale

Section 104.40: Non flasque quasicoherent sheaf associated to injective module

Section 104.41: A nonseparated flat group scheme

Section 104.42: A nonflat group scheme with flat identity component

Section 104.43: A nonseparated group algebraic space over a field

Section 104.44: Specializations between points in fibre étale morphism

Section 104.45: A torsor which is not an fppf torsor

Section 104.46: Stack with quasicompact flat covering which is not algebraic

Section 104.47: Limit preserving on objects, not limit preserving

Section 104.48: A nonalgebraic classifying stack

Section 104.49: Sheaf with quasicompact flat covering which is not algebraic

Section 104.50: Sheaves and specializations

Section 104.51: Sheaves and constructible functions

Section 104.52: The lisseétale site is not functorial

Section 104.53: Derived pushforward of quasicoherent modules

Section 104.54: A big abelian category

Section 104.55: Weakly associated points and scheme theoretic density

Section 104.56: Example of nonadditivity of traces

Section 104.57: Being projective is not local on the base

Section 104.58: Descent data for schemes need not be effective, even for a projective morphism

Section 104.59: A family of curves whose total space is not a scheme

Section 104.60: Derived base change

Section 104.61: An interesting compact object

Section 104.62: Two differential graded categories

Section 104.63: The stack of proper algebraic spaces is not algebraic

Section 104.64: An example of a nonalgebraic Homstack

Section 104.65: An algebraic stack not satisfying strong formal effectiveness

Section 104.66: A counter example to Grothendieck's existence theorem

Section 104.67: Affine formal algebraic spaces

Section 104.68: Flat maps are not directed limits of finitely presented flat maps

Section 104.69: The category of modules modulo torsion modules

Section 104.70: Different colimit topologies

Section 104.71: Universally submersive but not V covering

Section 104.72: The spectrum of the integers is not quasicompact