Theorems · Definition · algebraic geometry
CommAlgCat.FiniteEtale.finiteSpec
(k : Type u) → [inst : Field k] → CategoryTheory.Functor (CommAlgCat.FiniteEtale k)ᵒᵖ FintypeCat
If k is a field, this is the Spec functor sending a finite étale k-algebra R
to its finite prime spectrum.
- Defined in
- Mathlib.RingTheory.Etale.Finite
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functorstatement · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- Fieldstatement and proof · cited by 7,404
- Finitestatement · cited by 3,029
- Opposite.unopproof · cited by 2,231
- CategoryTheory.ObjectProperty.FullSubcategory.objproof · cited by 1,316
- Quiver.Hom.unopproof · cited by 903
- CategoryTheory.InducedCategory.Hom.homproof · cited by 850
- RingHomClass.toRingHomproof · cited by 746
- PrimeSpectrumproof · cited by 625
- FintypeCatstatement · cited by 217
Cited by6
Results whose statement or proof uses this declaration.
- CommAlgCat.FiniteEtale.equivOfIsSepClosedproof · cited by 3
- CommAlgCat.FiniteEtale.fiberIsoCompstatement · cited by 0
- CommAlgCat.FiniteEtale.fiberIsoFiniteSpecstatement · cited by 0
- CommAlgCat.FiniteEtale.finiteSpec_mapstatement and proof · cited by 0
- CommAlgCat.FiniteEtale.finiteSpec_obj_objstatement and proof · cited by 0
- CommAlgCat.FiniteEtale.equivOfIsSepClosed_functorstatement · cited by 0