Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Polynomial.imageOfDf_eq_comap_C_compl_zeroLocus
∀ {R : Type u_1} [inst : CommRing R] {f : Polynomial R},
AlgebraicGeometry.Polynomial.imageOfDf f = PrimeSpectrum.comap Polynomial.C '' (PrimeSpectrum.zeroLocus {f})ᶜThe open set imageOfDf f coincides with the image of basicOpen f under the
morphism C⁺ : Spec R[x] → Spec R.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- SetLike.coeproof · cited by 8,199
- Polynomialstatement and proof · cited by 5,681
- Set.imagestatement and proof · cited by 5,609
- Compl.complstatement and proof · cited by 2,925
- Set.extproof · cited by 2,266
- Polynomial.Cstatement and proof · cited by 1,598
- Polynomial.coeffproof · cited by 1,045
- Ideal.mapproof · cited by 692
- PrimeSpectrumstatement and proof · cited by 625
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