Theorems · Theorem · algebraic geometry
PrimeSpectrum.gc
∀ (R : Type u) [inst : CommSemiring R], GaloisConnection (fun I => PrimeSpectrum.zeroLocus ↑I) fun t => PrimeSpectrum.vanishingIdeal t
zeroLocus and vanishingIdeal form a Galois connection.
- Defined in
- Mathlib.RingTheory.Spectrum.Prime.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 67 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 and proof · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement · cited by 8,199
- Idealstatement and proof · cited by 4,748
- OrderDualstatement and proof · cited by 927
- PrimeSpectrumstatement and proof · cited by 625
- GaloisConnectionstatement · cited by 253
- PrimeSpectrum.zeroLocusstatement · cited by 164
- PrimeSpectrum.vanishingIdealstatement · cited by 36
- PrimeSpectrum.subset_zeroLocus_iff_le_vanishingIdealproof · cited by 3
Cited by14
Results whose statement or proof uses this declaration.
- PrimeSpectrum.zeroLocus_vanishingIdeal_eq_closureproof · cited by 11
- PrimeSpectrum.gc_setproof · cited by 7
- PrimeSpectrum.zeroLocus_radicalproof · cited by 6
- PrimeSpectrum.zeroLocus_botproof · cited by 5
- PrimeSpectrum.vanishingIdeal_closureproof · cited by 3
- PrimeSpectrum.vanishingIdeal_anti_monoproof · cited by 2
- PrimeSpectrum.zeroLocus_anti_mono_idealproof · cited by 2
- PrimeSpectrum.zeroLocus_supproof · cited by 2
- PrimeSpectrum.subset_zeroLocus_vanishingIdealproof · cited by 1
- PrimeSpectrum.zeroLocus_iSupproof · cited by 0
- PrimeSpectrum.le_vanishingIdeal_zeroLocusproof · cited by 0
- PrimeSpectrum.vanishingIdeal_emptyproof · cited by 0