Theorems · Definition · algebraic geometry
MvPolynomial.zeroLocus
{k : Type u_1} →
(K : Type u_2) →
[inst : Field k] → [inst_1 : Field K] → [Algebra k K] → {σ : Type u_3} → Ideal (MvPolynomial σ k) → Set (σ → K)Set of points that are zeroes of all polynomials in an ideal
- Defined in
- Mathlib.RingTheory.Nullstellensatz
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Set.ofPredproof · cited by 6,101
- Finsuppstatement · cited by 5,255
- Idealstatement and proof · cited by 4,748
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.aevalproof · cited by 298
Cited by15
Results whose statement or proof uses this declaration.
- MvPolynomial.le_vanishingIdeal_zeroLocusstatement and proof · cited by 3
- FirstOrder.Ring.mvPolynomial_zeroLocus_definablestatement · cited by 1
- MvPolynomial.zeroLocus_anti_monostatement and proof · cited by 1
- MvPolynomial.zeroLocus_botstatement · cited by 1
- MvPolynomial.zeroLocus_spanstatement · cited by 1
- MvPolynomial.vanishingIdeal_zeroLocus_eq_radicalstatement and proof · cited by 1
- MvPolynomial.zeroLocus_vanishingIdeal_galoisConnectionstatement · cited by 1
- MvPolynomial.zeroLocus_vanishingIdeal_lestatement · cited by 1
- ax_grothendieck_zeroLocusstatement and proof · cited by 1
- MvPolynomial.radical_le_vanishingIdeal_zeroLocusstatement and proof · cited by 1
- MvPolynomial.le_zeroLocus_iff_le_vanishingIdealstatement · cited by 1
- MvPolynomial.pointToPoint_zeroLocus_lestatement and proof · cited by 0