Mathlib Map

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
Assumes
FieldFieldAlgebra

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MvPolynomial.le_vanishingIdeal_zeroLocus · cited by 3MvPolynomial.le_vanishing…FirstOrder.Ring.mvPolynomial_zeroLocus_definable · cited by 1Ring.mvPolynomial_zeroLoc…MvPolynomial.zeroLocus_anti_mono · cited by 1MvPolynomial.zeroLocus_an…MvPolynomial.zeroLocus_bot · cited by 1MvPolynomial.zeroLocus_botMvPolynomial.zeroLocus_span · cited by 1MvPolynomial.zeroLocus_sp…MvPolynomial.vanishingIdeal_zeroLocus_eq_radical · cited by 1MvPolynomial.vanishingIde…MvPolynomial.zeroLocus_vanishingIdeal_galoisConnection · cited by 1MvPolynomial.zeroLocus_va…MvPolynomial.zeroLocus_vanishingIdeal_le · cited by 1MvPolynomial.zeroLocus_va…ax_grothendieck_zeroLocus · cited by 1ax_grothendieck_zeroLocusMvPolynomial.radical_le_vanishingIdeal_zeroLocus · cited by 1MvPolynomial.radical_le_v…MvPolynomial.le_zeroLocus_iff_le_vanishingIdeal · cited by 1MvPolynomial.le_zeroLocus…MvPolynomial.pointToPoint_zeroLocus_le · cited by 0MvPolynomial.pointToPoint…MvPolynomial.zeroLocus_top · cited by 0MvPolynomial.zeroLocus_topMvPolynomial.mem_zeroLocus_iff · cited by 0MvPolynomial.mem_zeroLocu…MvPolynomial.IsPrime.vanishingIdeal_zeroLocus · cited by 0IsPrime.vanishingIdeal_ze…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetAlgebra · cited by 11388AlgebraField · cited by 7404FieldSet.ofPred · cited by 6101Set.ofPredFinsupp · cited by 5255FinsuppIdeal · cited by 4748IdealMvPolynomial · cited by 2140MvPolynomialMvPolynomial.aeval · cited by 298MvPolynomial.aevalMvPolynomial.zeroLocusCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by15

Results whose statement or proof uses this declaration.