Theorems · Theorem · algebraic geometry
PrimeSpectrum.gc_set
∀ (R : Type u) [inst : CommSemiring R], GaloisConnection (fun s => PrimeSpectrum.zeroLocus s) fun t => ↑(PrimeSpectrum.vanishingIdeal t)
zeroLocus and vanishingIdeal form a Galois connection.
- Defined in
- Mathlib.RingTheory.Spectrum.Prime.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 68 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement and proof · cited by 8,199
- Idealstatement · cited by 4,748
- Ideal.spanproof · cited by 948
- OrderDualstatement and proof · cited by 927
- PrimeSpectrumstatement and proof · cited by 625
- GaloisConnectionstatement and proof · cited by 253
- PrimeSpectrum.zeroLocusstatement · cited by 164
- GaloisInsertion.gcproof · cited by 137
- PrimeSpectrum.vanishingIdealstatement and proof · cited by 36
- PrimeSpectrum.zeroLocus_spanproof · cited by 17
Cited by7
Results whose statement or proof uses this declaration.
- PrimeSpectrum.zeroLocus_iUnionproof · cited by 4
- PrimeSpectrum.zeroLocus_iUnion₂proof · cited by 3
- PrimeSpectrum.zeroLocus_anti_monoproof · cited by 3
- PrimeSpectrum.zeroLocus_unionproof · cited by 2
- PrimeSpectrum.subset_zeroLocus_iff_subset_vanishingIdealproof · cited by 2
- PrimeSpectrum.zeroLocus_emptyproof · cited by 1
- PrimeSpectrum.subset_vanishingIdeal_zeroLocusproof · cited by 0