Theorems · Theorem · algebraic geometry
IsLocalRing.specializes_closedPoint
∀ {R : Type u} [inst : CommSemiring R] [inst_1 : IsLocalRing R] (x : PrimeSpectrum R), x ⤳ IsLocalRing.closedPoint R- Cited by
- 6 results in Mathlib
- Foundations
- Depth 83 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.
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
- PrimeSpectrumstatement and proof · cited by 625
- IsLocalRingstatement and proof · cited by 339
- Specializesstatement · cited by 176
- IsLocalRing.closedPointstatement and proof · cited by 60
- Ideal.IsPrime.ne_top'proof · cited by 38
- IsLocalRing.le_maximalIdealproof · cited by 20
- PrimeSpectrum.le_iff_specializesproof · cited by 8
Cited by6
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.ValuativeCriterion.Existence.specializingMapproof · cited by 1
- IsLocalRing.closed_point_mem_iffproof · cited by 1
- AlgebraicGeometry.ValuativeCriterion.Existence.of_specializingMapproof · cited by 1
- IsLocalRing.closedPoint_mem_iffproof · cited by 0
- AlgebraicGeometry.Scheme.range_fromSpecStalkproof · cited by 0
- AlgebraicGeometry.pointsPi_surjectiveproof · cited by 0