Theorems · Theorem · algebraic geometry
IsLocalRing.comap_closedPoint
∀ {R : Type u} [inst : CommSemiring R] [inst_1 : IsLocalRing R] {S : Type v} [inst_2 : CommSemiring S]
[inst_3 : IsLocalRing S] (f : R →+* S) [IsLocalHom f],
PrimeSpectrum.comap f (IsLocalRing.closedPoint S) = IsLocalRing.closedPoint R- Cited by
- 4 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- PrimeSpectrumstatement · cited by 625
- IsLocalRingstatement and proof · cited by 339
- PrimeSpectrum.comapstatement · cited by 199
- IsLocalHomstatement and proof · cited by 100
- IsLocalRing.closedPointstatement · cited by 60
- IsLocalRing.isLocalHom_iff_comap_closedPointproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq_comapproof · cited by 1
- AlgebraicGeometry.Spec_closedPointproof · cited by 1
- AlgebraicGeometry.IsAffineOpen.isoSpec_hom_applyproof · cited by 1
- AlgebraicGeometry.ValuativeCriterion.Existence.specializingMapproof · cited by 1