Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.geometricFiber
(Ω : Type u) → [inst : Field Ω] → [IsSepClosed Ω] → AlgebraicGeometry.Scheme.etaleTopology.Point
A separably closed field Ω defines a point on the étale topology by the fiber
functor X ↦ Hom(Spec Ω, X).
- Defined in
- Mathlib.AlgebraicGeometry.Sites.Etale
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldIsSepClosed
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- Fieldstatement and proof · cited by 7,404
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- AlgebraicGeometry.Specproof · cited by 626
- CategoryTheory.Sieveproof · cited by 552
- CategoryTheory.coyonedaproof · cited by 208
- CategoryTheory.GrothendieckTopology.Pointstatement · cited by 123
- IsSepClosedstatement and proof · cited by 41
- AlgebraicGeometry.Scheme.etaleTopologystatement and proof · cited by 2
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