Theorems · Definition · algebraic geometry
CommAlgCat.FiniteEtale.fiberIsoFiniteSpec
(Ω : Type w) → [inst : Field Ω] → [IsSepClosed Ω] → CommAlgCat.FiniteEtale.fiber Ω Ω ≅ CommAlgCat.FiniteEtale.finiteSpec Ω
If Ω is separably closed, the fiber functor for finite étale Ω-algebras
is naturally isomorphic to the (finite) Spec functor.
- Defined in
- Mathlib.RingTheory.Etale.Finite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 203 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.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Functorstatement · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- Fieldstatement and proof · cited by 7,404
- CategoryTheory.Isostatement · cited by 3,963
- Finitestatement · cited by 3,029
- Opposite.unopproof · cited by 2,231
- CategoryTheory.ObjectProperty.FullSubcategory.objproof · cited by 1,316
- FintypeCatstatement · cited by 217
- CategoryTheory.NatIso.ofComponentsproof · cited by 178
- CommAlgCatstatement · cited by 96
- CommAlgCat.carrierproof · cited by 77
Cited by1
Results whose statement or proof uses this declaration.
- CommAlgCat.FiniteEtale.fiberIsoCompproof · cited by 0