Theorems · Definition · algebraic geometry
IsLocalRing.closedPoint
(R : Type u) → [inst : CommSemiring R] → [IsLocalRing R] → PrimeSpectrum R
The closed point in the prime spectrum of a local ring.
- Cited by
- 60 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringIsLocalRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- PrimeSpectrumstatement · cited by 625
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealproof · cited by 297
Cited by66
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.stalkClosedPointTostatement and proof · cited by 17
- AlgebraicGeometry.stalkClosedPointIsostatement and proof · cited by 9
- AlgebraicGeometry.Scheme.SpecToEquivOfFieldproof · cited by 8
- AlgebraicGeometry.Scheme.fromSpecStalk_closedPointstatement · cited by 7
- IsLocalRing.specializes_closedPointstatement and proof · cited by 6
- IsLocalRing.comap_closedPointstatement · cited by 4
- AlgebraicGeometry.LocallyRingedSpace.toΓSpecFunproof · cited by 4
- AlgebraicGeometry.Scheme.germ_stalkClosedPointTostatement and proof · cited by 4
- AlgebraicGeometry.pointEquivClosedPointproof · cited by 4
- AlgebraicGeometry.Scheme.preimage_eq_top_of_closedPoint_memstatement and proof · cited by 4
- AlgebraicGeometry.Scheme.Spec_stalkClosedPointTo_fromSpecStalkstatement and proof · cited by 3
- AlgebraicGeometry.spread_out_of_isGermInjective'proof · cited by 3