Theorems · Theorem · algebraic geometry
PrimeSpectrum.basicOpen_eq_zeroLocus_compl
∀ {R : Type u} [inst : CommSemiring R] (r : R), ↑(PrimeSpectrum.basicOpen r) = (PrimeSpectrum.zeroLocus {r})ᶜ- Cited by
- 34 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement · cited by 8,199
- Compl.complstatement · cited by 2,925
- Set.extproof · cited by 2,266
- TopologicalSpace.Opensstatement · cited by 2,040
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.asIdealproof · cited by 333
- PrimeSpectrum.zeroLocusstatement and proof · cited by 164
- PrimeSpectrum.basicOpenstatement · cited by 163
Cited by34
Results whose statement or proof uses this declaration.
- PrimeSpectrum.localization_away_comap_rangeproof · cited by 17
- PrimeSpectrum.isTopologicalBasis_basic_opensproof · cited by 11
- PrimeSpectrum.basicOpen_oneproof · cited by 7
- PrimeSpectrum.iSup_basicOpen_eq_top_iffproof · cited by 6
- PrimeSpectrum.basicOpen_mulproof · cited by 5
- PrimeSpectrum.basicOpen_eq_zeroLocus_of_mul_addproof · cited by 4
- PrimeSpectrum.mem_image_comap_basicOpenproof · cited by 3
- Algebra.basicOpen_subset_etaleLocus_iffproof · cited by 3
- Algebra.basicOpen_subset_smoothLocus_iffproof · cited by 3
- Algebra.basicOpen_subset_unramifiedLocus_iffproof · cited by 3
- Algebra.IsLocalIso.of_span_range_eq_topproof · cited by 3
- PrimeSpectrum.comap_evalRingHom_basicOpenproof · cited by 2