Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.smallEtaleTopology
(X : AlgebraicGeometry.Scheme) → CategoryTheory.GrothendieckTopology X.Etale
The small étale site of a scheme is the Grothendieck topology on the
category of schemes étale over X induced from the étale topology on Scheme.{u}.
- Defined in
- Mathlib.AlgebraicGeometry.Sites.Etale
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.GrothendieckTopologystatement · cited by 1,415
- AlgebraicGeometry.Etaleproof · cited by 27
- AlgebraicGeometry.Scheme.Etalestatement · cited by 16
- AlgebraicGeometry.Scheme.smallGrothendieckTopologyproof · cited by 3
Cited by13
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.pointSmallEtalestatement and proof · cited by 7
- AlgebraicGeometry.Scheme.pointSmallEtaleFiberObjToPreimagestatement · cited by 4
- AlgebraicGeometry.Scheme.ofArrows_mem_smallEtaleTopology_iffstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.pointSmallEtaleFiberObjToPreimage_coestatement · cited by 1
- AlgebraicGeometry.Scheme.isConservative_pointSmallEtalestatement · cited by 1
- AlgebraicGeometry.Scheme.pointSmallEtaleFiberObjToPreimage_surjectivestatement · cited by 1
- AlgebraicGeometry.Scheme.AffineEtale.sheafEquivstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.AffineEtale.topologyproof · cited by 1
- AlgebraicGeometry.Scheme.isConservativeFamilyOfPoints_pointSmallEtale'statement · cited by 0
- AlgebraicGeometry.Scheme.pointSmallEtale_fiberstatement · cited by 0
- AlgebraicGeometry.Scheme.pointSmallEtale.congr_simpstatement · cited by 0
- AlgebraicGeometry.Scheme.pointSmallEtaleFiberObjToPreimage.congr_simpstatement · cited by 0