Theorems · Definition · algebraic geometry
PrimeSpectrum.basicOpen
{R : Type u} → [inst : CommSemiring R] → R → TopologicalSpace.Opens (PrimeSpectrum R)basicOpen r is the open subset containing all prime ideals not containing r.
- Cited by
- 163 results in Mathlib
- Foundations
- Depth 77 from the axioms, rests on 981 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Set.ofPredproof · cited by 6,101
- TopologicalSpace.Opensstatement · cited by 2,040
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.asIdealproof · cited by 333
Cited by174
Results whose statement or proof uses this declaration.
- PrimeSpectrum.basicOpen_eq_zeroLocus_complstatement · cited by 34
- AlgebraicGeometry.StructureSheaf.conststatement and proof · cited by 20
- AlgebraicGeometry.IsAffineOpen.basicOpenproof · cited by 19
- AlgebraicGeometry.IsAffineOpen.isLocalization_basicOpenproof · cited by 18
- PrimeSpectrum.localization_away_comap_rangestatement and proof · cited by 17
- PrimeSpectrum.isBasis_basic_opensstatement and proof · cited by 16
- PrimeSpectrum.isTopologicalBasis_basic_opensstatement and proof · cited by 11
- AlgebraicGeometry.Scheme.Modules.fromTildeΓproof · cited by 9
- PrimeSpectrum.basicOpen_onestatement · cited by 7
- AlgebraicGeometry.Proj.toBasicOpenOfGlobalSectionsproof · cited by 7
- AlgebraicGeometry.basicOpenIsoSpecAwaystatement and proof · cited by 7
- AlgebraicGeometry.Scheme.toSpecΓ_preimage_basicOpenstatement · cited by 7