Theorems · Theorem · algebraic geometry
AlgebraicGeometry.residueFieldIsoBase.congr_simp
∀ {X : AlgebraicGeometry.Scheme} {K : Type u} [inst : Field K] [inst_1 : IsAlgClosed K]
(f f_1 : X ⟶ AlgebraicGeometry.Spec (CommRingCat.of K)) (e_f : f = f_1)
[inst_2 : AlgebraicGeometry.LocallyOfFiniteType f] (x : ↥X) (hx : IsClosed {x}),
AlgebraicGeometry.residueFieldIsoBase f x hx = AlgebraicGeometry.residueFieldIsoBase f_1 x hx- Cited by
- 0 results in Mathlib
- Foundations
- Depth 226 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- Fieldstatement and proof · cited by 7,404
- CategoryTheory.Isostatement · cited by 3,963
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
- IsClosedstatement and proof · cited by 1,639
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